Thèses : « Modular representation »

1

Rahm, Jonas. « Biologically plausible visual representation of modular decomposition ». Thesis, University of Skövde, School of Humanities and Informatics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-953.

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Modular decompositions of protein interaction networks can be used to identify modules of cooperating proteins. The biological plausibility off these modules might be questioned though. This report describes how a modular decomposition can be completed with semantic information in the visual representation. Possible methods for creating modules of functionally related proteins are also proposed in this work. The results show that such modules, with advantage can be combined with modules from a graph decomposition, to find proteins that are likely to cooperate to perform certain functions in organisms

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2

MacQuarrie, John William. « The modular representation theory of profinite groups ». Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496232.

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Our aim is to transfer many of the foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a profinite group G, where kc is a finite field of characteristic p. Our approach is as follows. We define the concept of relative projectivity for a profinite module over k[[G]] and prove a characterization analogous to the finite case with additions of interest to the pro and sources for indecomposable finitely generated k[[G]]-modules, extending several results known to hold in the finite case. For sources this requires additional assumptions. We prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group, as well as a lesser known variant due to M.E. Harris. We give a version of the Green Correspondence for finitely generated modules over virtually pro-p groups.

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3

Rubio, y. Degrassi L. « On Hochschild cohomology and modular representation theory ». Thesis, City, University of London, 2016. http://openaccess.city.ac.uk/18406/.

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The aim of this thesis is to study local and global invariants in representation theory of finite groups using the (restricted) Lie algebra structure of the first degree of Hochschild cohomology of a block algebra B as a main tool. This lead to two directions: In the first part we investigate the global approach. In particular, we prove the compatibility of the p-power map under stable equivalence of Morita type of subclasses of the first Hochschild cohomology represented by integrable derivations. Further results in this aspect include an example showing that the p-power map cannot generally be expressed in terms of the BV operator. We also study some properties of r-integrable derivations and we provide a family of examples given by the quantum complete intersections where all the derivations are r-integrable. In the second part our attention is focused on the local invariants. More precisely, we fully characterise blocks B with unique isomorphism class of simple modules such that the first degree Hochschild cohomology HH1(B) is a simple as Lie algebra. In this case we prove that B is a nilpotent block with an elementary abelian defect group P of order at least 3 and HH1(B) is isomorphic to the Witt algebra HH1(kP).

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4

Martin, Stuart. « Quivers and the modular representation theory of finite groups ». Thesis, University of Oxford, 1988. http://ora.ox.ac.uk/objects/uuid:59d4dc72-60e5-4424-9e3c-650eb2b1d050.

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The purpose of this thesis is to discuss the rôle of certain types of quiver which appear in the modular representation theory of finite groups. It is our concern to study two different types of quiver. First of all we construct the ordinary quiver of certain blocks of defect 2 of the symmetric group, and then apply our results to the alternating group and to the theory of partitions. Secondly, we consider connected components of the stable Auslander-Reiten quiver of certain groups G with normal subgroup N. The main interest lies in comparing the tree class of components of N-modules, with the tree class of components of these modules induced up to G.

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5

Power, David James. « A library for parallel arithmetic using a modular representation ». Thesis, University of Bath, 2001. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341640.

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6

Carlisle, D. P. « The modular representation theory of GL(n,p) and applications ». Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374790.

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7

Suter, Rudolf. « First part : Representation rings and modular transformations ; Second part : Tensor products of simple Uq₍sl₂)-modules / ». Zürich, 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10878.

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8

Hauge, Martin. « Triangulated categories in modular representation theory and their direct sum decompositions ». Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.723477.

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9

Dunn-Davies, Hywel. « A Diagrammatic Formalism for the Modular Representation of Agent Interaction Protocols ». Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.511872.

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10

Wang, Tsomg-Niang 1953. « A modular prolog representation of a TCP protocol finite state machine ». Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276580.

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This paper describes a Protocol Finite State Machine (PFSM) for implementing communication protocols. Our objective is to develop and implement a general model for communication protocols based on the principles of finite state machines and make the design of transport entity more modular and easier to maintain and modify. We have designed an inference method and knowledge representation, based on semantic networks, for implementing this model. We have added interactive capability and automatic error detection to check for invalid external events and other types of errors in our model. PFSM consists of one or more knowledge bases depicting the state machine model for each communication protocol, an inference engine that uses the knowledge base(s), a working memory, a knowledge acquisition subsystem to gather the data required to build the knowledge base(s), a dialog subsystem to conduct an interactive conversation with the user(s), and an explanation subsystem to explain the inferencing mechanism. (Abstract shortened with permission of author.)

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11

Nguyen, Christopher Dinh. « Fast modular exponentiation using residue domain representation| A hardware implementation and analysis ». Thesis, University of Maryland, Baltimore County, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1551346.

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Using modular exponentiation as an application, we engineered on FPGA fabric and analyzed the first implementation of two arithmetic algorithms in Reduced-Precision Residue Number Systems (RP-RNS): the partial-reconstruction algorithm and quotient-first scaling algorithm. Residue number systems (RNS) provide an alternative representation to the binary system for computation. They offer full parallel computation for addition, subtraction, and multiplication. However, base extension, division, and sign detection become harder operations. Phatak's RP-RNS uses a time-memory trade-off to achieve O(lg N) running time for base extension and scaling, where N is the bit-length of the operands, compared with Kawamura's Cox-Rower architecture and its derivatives, which appear to take O(N) steps and therefore O(N) delay to the best of our knowledge. We implemented the fully parallel RP-RNS architecture based on Phatak's description and architecture diagrams. Our design decisions included distributing the lookup tables among each channel, removing the adder trees, and removing the parallel table access thus trading size for speed. In retrospect, we should have hosted the tables in memory off the FPGA. We measured the FPGA utilization, storage size, and cycle counts. The data we present, though less than optimal, confirms the theoretical trends calculated by Phatak. FPGA utilization grows proportional K log(K) where K is the number of hardware channels. Storage grows proportional to O(N

3 lg lg N). When using Phatak's recommendations,cycle count grows proportional to O(lg N). Our contributions include documentation of our design, architecture, and implementation; a detailed testing methodology; and performance data based on our implementation to enable others to replicate our implementation and findings.

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12

高木, 直史, et Naofumi Takagi. « A hardware algorithm for modular multiplication/division ». IEEE, 2005. http://hdl.handle.net/2237/5293.

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13

Hazi, Amit. « Semisimple filtrations of tilting modules for algebraic groups ». Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/271774.

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Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. The indecomposable tilting modules $\{T(\lambda)\}$ for $G$, which are labeled by highest weight, form an important class of self-dual representations over $k$. In this thesis we investigate semisimple filtrations of minimal length (Loewy series) of tilting modules. We first demonstrate a criterion for determining when tilting modules for arbitrary quasi-hereditary algebras are rigid, i.e. have a unique Loewy series. Our criterion involves checking that $T(\lambda)$ does not have certain subquotients whose composition factors extend more than one layer in the radical or socle series. We apply this criterion to show that the restricted tilting modules for $SL_4$ are rigid when $p \geq 5$, something beyond the scope of previous work on this topic by Andersen and Kaneda. Even when $T(\lambda)$ is not rigid, in many cases it has a particularly structured Loewy series which we call a balanced semisimple filtration, whose semisimple subquotients or "layers" are symmetric about some middle layer. Balanced semisimple filtrations also suggest a remarkably straightforward algorithm for calculating tilting characters from the irreducible characters. Applying Lusztig's character formula for the simple modules, we show that the algorithm agrees with Soergel's character formula for the regular indecomposable tilting modules for quantum groups at roots of unity. We then show that these filtrations really do exist for these tilting modules. In the modular case, high weight tilting modules exhibit self-similarity in their characters at $p$-power scales. This is due to what we call higher-order linkage, an old character-theoretic result relating modular tilting characters and quantum tilting characters at $p$-power roots of unity. To better understand this behavior we describe an explicit categorification of higher-order linkage using the language of Soergel bimodules. Along the way we also develop the algebra and combinatorics of higher-order linkage at the de-categorified level. We hope that this will provide a foundation for a tilting character formula valid for all weights in the modular case when $p$ is sufficiently large.

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14

Pedrotti, Vagner 1980. « Decomposição modular de grafos não orientados ». [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276072.

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Orientador: Celia Picinin de Mello
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação
Made available in DSpace on 2018-08-08T21:07:02Z (GMT). No. of bitstreams: 1 Pedrotti_Vagner_M.pdf: 1466848 bytes, checksum: 52ed7d36d9f4f7cb6bee307b689f5f78 (MD5) Previous issue date: 2007
Resumo: Um modulo de um grafo é um subconjunto de seus vertices que não é diferenciado, em relação à adjancencia peços demais vertices do mesmo grafo. Dado um mpodulo M de um grafo G, se todo módulo de G que intercepta M está contido nele ou o contém. M é denominado módulo forte¿Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital
Abstract: A module of a graph is a non distinguishable subset of nodes, regarding the nodes adjacency. Let M denote any module of a graph G. If every module of G wich overlaps M either contains M or is included in it, M is called a strong module...Note: The complete abstract is available with the full electronic digital thesis or dissertations
Mestrado
Teoria da Computação
Mestre em Ciência da Computação

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15

Ko, W. Y. Albert, et 高永賢. « The design of a representation and analysis method for modular self-reconfigurable robots ». Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29513807.

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16

Ren-He, Su. « The Kohnen plus space for Hilbert-Siegel modular forms ». 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215374.

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17

McCorkindale, Jane. « The 2-modular representation theory of PSUâ†3(q), q #ident to# 3(mod 4) ». Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279980.

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18

Yuliawan, Fajar Verfasser], et Henning [Akademischer Betreuer] [Krause. « Actions of Hochschild Cohomology and Local Duality in Modular Representation Theory / Fajar Yuliawan ; Betreuer : Henning Krause ». Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/115018177X/34.

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19

CHINELLO, GIANMARCO. « Représentations l-modulaires des groupes p-adiques. Décomposition en blocs de la catégorie des représentations lisses de GL(m,D), groupe métaplectique et représentation de Weil ». Doctoral thesis, Université de Versailles St-Quentin-en-Yvelines, 2015. http://hdl.handle.net/10281/123569.

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This thesis focuses on two problems on l-modular representation theory of p-adic groups. Let F be a non-archimedean local field of residue characteristic p different from l. In the first part, we study block decomposition of the category of smooth modular representations of GL(n; F) and its inner forms.We want to reduce the description of a positive-level block to the description of a 0-level block (of a similar group) seeking equivalences of categories. Using the type theory of Bushnell-Kutzko in the modular case and a theorem of category theory, we reduce the problem to find an isomorphism between two intertwining algebras. The proof of the existence of such an isomorphism is not complete because it relies on a conjecture that we state and we prove for several cases. In the second part we generalize the construction of metaplectic group and Weil representation in the case of representations over un integral domain. We define a central extension of the symplectic group over F by the multiplicative group of an integral domain. We prove that it satisfies the same properties as in the complex case.
Cette thèse traite deux problèmes concernant la théorie des représentations l-modulaires d’un groupe p-adique. Soit F un corps local non archimédien de caractéristique résiduelle p différente de l. Dans la première partie, on étudie la décomposition en blocs de la catégorie des représentations lisses `-modulaires de GL(n; F) et de ses formes intérieures. On veut ramener la description d’un bloc de niveau positif à celle d’un bloc de niveau 0 (d’un autre groupe du même type) en cherchant des équivalences de catégories. En utilisant la théorie des types de Bushnell-Kutzko dans le cas modulaire et un théorème de la théorie des catégories, on se ramene à trouver un isomorphisme entre deux algèbres d’entrelacement. La preuve de l’existence d’un tel isomorphisme n’est pas complète car elle repose sur une conjecture qu’on énonce et qui est prouvée pour plusieurs cas. Dans une deuxième partie on généralise la construction du groupe métaplectique et de la représentation de Weil dans le cas des représentations sur un anneau intègre. On construit une extension centrale du groupe symplectique sur F par le groupe multiplicatif d’un anneau intègre et on prouve qu’il satisfait les mêmes propriétés que dans le cas des représentations complexes.

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20

Turchetti, Danièle. « Contributions to arithmetic geometry in mixed characteristic : lifting covers of curves, non-archimedean geometry and the l-modular Weil representation ». Thesis, Versailles-St Quentin en Yvelines, 2014. http://www.theses.fr/2014VERS0022/document.

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Dans cette thèse on étudie certains phénomènes d'interactions entre caractéristique positive et caractéristique nulle. Dans un premier temps on s'occupe du problème de relèvement locale d'actions de groupes. On y montre des conditions nécessaires pour l'existence de relèvement de certains actions du groupe Z/pZ x Z/pZ. Pour une action d'un groupe fini quelconque, on y étudie les arbres de Hurwitz, en montrant que chaque arbre de Hurwitz admet un plongement dans le disque unitaire fermé de Berkovich et que ses données de Hurwitz peuvent être décrites de façon analytique. Dans une deuxième partie nous construisons un analogue de la représentation de Weil à coefficients dans un anneau intègre, et nous montrons que cela satisfait les mêmes propriétés que dans le cas de coefficients complexes
In this thesis, we study the interplay between positive and zero characteristic. In a first instance, we deal with the local lifting problem of lifting actions of curves. We show necessary conditions for the existence of liftings of some actions of Z/pZ x Z/pZ. Then, for an action of a general finite group, we study the associated Hurwitz tree, showing that every Hurwitz tree has a canonical metric embedding in the Berkovich closed unit disc, and that the Hurwitz data can be described analytically.In the last chapter, we define an analog of the Weil representation with coefficients in an integral domain, showing that such representation satisfies the same properties than in the case with complex coefficients

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21

Wild, Marcel Wolfgang. « Dreieckverbande : lineare und quadratische darstellungstheorie ». Thesis, University of Zurich, 1987. http://hdl.handle.net/10019.1/70322.

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Prof. Marcel Wild completed his PhD with Zurick University and this is a copy of the original works
The original works can be found at http://www.hbz.uzh.ch/
ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school (Wille, Herrmann, Poguntke, et al), to large extent triggered by the linear representations of posets (Gabriel, Gelfand-Ponomarev, Nazarova, Roiter, Brenner, et al). Even though posets are more general than lattices, none of the two theories encompasses the other. In my thesis a natural type of finite lattice is identified, i.e. triangle lattices, and their linear representation theory is advanced. All of this was triggered by a more intricate setting of quadratic spaces (as opposed to mere vector spaces) and the question of how Witt’s Theorem on the congruence of finite-dimensional quadratic spaces lifts to spaces of uncountable dimensions. That issue is dealt with in the second half of the thesis.

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22

Juteau, Daniel. « Correspondance de Springer modulaire et matrices de décomposition ». Phd thesis, Université Paris-Diderot - Paris VII, 2007. http://tel.archives-ouvertes.fr/tel-00355559.

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In 1976, Springer defined a correspondence making a link between the irreducible ordinary (characteristic zero) representations of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (for example the symmetric group) are particular cases of decomposition numbers for equivariant perverse sheaves on the nilpotent variety. We calculate explicitly the decomposition numbers associated to the regular and subregular classes, and to the minimal and trivial classes. We determine the correspondence explicitly in the case of the symmetric group, and show that James's row and column removal rule is a consequence of a smooth equivalence of nilpotent singularities obtained by Kraft and Procesi. The first chapter contains generalities about perverse sheaves with Z_l and F_l coefficients.

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23

Towers, Matthew John. « Modular representations of p-groups ». Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427611.

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Buzzard, Kevin. « The levels of modular representations ». Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362978.

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Wildon, Mark. « Modular representations of symmetric groups ». Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403775.

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26

Trias, Justin. « Correspondance thêta locale ℓ-modulaire ». Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS380.

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Soit F un corps local non archimédien de caractéristique différente de 2 et de caractéristique résiduelle p. La correspondance thêta locale sur F établit une bijection entre des sous-ensembles de représentations lisses irréductibles complexes d’un premier groupe réductif H et d’un second groupe réductif H0, où (H,H0) forme une paire duale dans un groupe symplectique. Soit R un corps de caractéristique ℓ positive différente de p. Dans ce travail, on donne des conditions minimales sur R pour généraliser le théorème de Stone-von Neumann au cas des représentations modulaires i.e. à coefficients dans R. Cela permet ensuite de construire la représentation de Weil modulaire qui vérifie des propriétés analogues au cas complexe [MVW87]. Quand R est algébriquement clos, on généralise la preuve de la correspondance classique pour les paires duales non quaternioniques [GT16] sous deux hypothèses. La première est que ℓ soit suffisamment grand vis-à-vis d’une borne explicite dépendant des pro-ordres H1 et H2. La seconde est une hypothèse qui résulterait d’une meilleure connaissance de la théorie des opérateurs d’entrelacement dans le cas modulaire
Let F be a local non archimedean field of characteristic not 2 and residual characteristic p. The local theta correspondence over F gives a bijection between some subsets of irreductible smooth complex reprensentations of a first reductive group H and a second reductive group H0, where (H,H0) is a dual pair in a symplectic group. Let R be a field of characteristic ℓ different from p. In this thesis, we give minimal conditions on R so thatStone-von Neumann’s theorem can be generalised in the setting of modular representation theory, which means when the coefficient field is R. This generalisation enables to define a modular Weil representation which verifies analogous properties to that of the complex case [MVW87]. When R is algebraically closed, we generalise the proof of the classical correspondence for non quaternionic dual pairs [GT16] under two assumptions. Firstly,the characteristic ℓ has to be greater than a certain explicit bound which depends on the pro-orders of H1 and H2. The second hypothesis have a deep connection to the theory of intertwining and would result from a better understanding of that theory in the modular setting

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Russell, Lee. « Modular representations of the symmetric group ». Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627178.

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Yaseen, Abdul Kareem Abdul Rahman. « Modular spin representations of the symmetric group ». Thesis, Aberystwyth University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491551.

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Tsaknias, Panagiotis I. « On higher congruences of modular Galois representations ». Thesis, University of Sheffield, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.522367.

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Jarvis, Ashley Frazer. « On Galois representations associated to Hilbert modular forms ». Thesis, University of Cambridge, 1994. https://www.repository.cam.ac.uk/handle/1810/251724.

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Campbell, Peter Steven. « Permutation modules and representation theory ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ60107.pdf.

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Sin, P. K. W. « Some problems on induced modular representations of finite groups ». Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375304.

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Tickner, Suzanne. « Projective modular representations of certain classes of finite groups ». Thesis, University of Liverpool, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317291.

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Parsons, Christopher M. « Modular representations and invariants of elementary abelian p-groups ». Thesis, University of Kent, 2018. https://kar.kent.ac.uk/69138/.

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The purpose of this thesis is to develop tools to more easily classify the modular representations of elementary abelian p-groups and better understand their invariant rings. Since these groups almost always have wild representation type complete classification of the indecomposables is considered impossible and as such an alternative perspective is required. We reformulate the representation classification in the perspective of classifying maximal abelian subgroups of unipotent groups. Thence we express the problem as determining finitely many 'covering' homomorphisms of the form σ : (F^d, +) → GL_n(F) whose images collectively contain the images of all such representations up to equivalence. To aid in this we attach a combinatorial equivalence invariant object to modular p-group representations thereby allowing us to segment the problem and more easily distinguish between inequivalent families. Using these tools we build upon the work of [11] and develop a full set of covering homomorphisms for all modular elementary abelian p-groups in GL_4(F), GL_5(F) and GL_6(F). In doing so we also provide covering homomorphisms for select families in arbitrary dimension with specific patterns in their combinatorial invariant. By way of example we use these to provide an explicit construction for the Sylow p-subgroups of the finite orthogonal groups. Thereafter our focus switches to invariant rings. Given a matrix group in the image of a homomorphism σ : (F^d, +) → GL_n(F) we explore methods of recovering the W ≤ (F^d, +) used to generate the group purely through its action on specific elements in the symmetric algebra of the dual, properties of which are indicative of properties of the invariant ring. Using this we provide an alternative explicit construction for the invariant rings implicitly generated in [8]. Further we generalise a long-exploited technique for inductively defining invariants from those of maximal subgroups. After classifying the invariant rings and fields of several hitherto classified families we focus on the four-dimensional modular elementary abelian p-groups with rank 2, providing their invariant rings if Cohen-Macaulay and algorithmic methods to procure it otherwise.

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Phillips, Aaron M. « Restricting modular spin representations of symmetric and alternating groups / ». view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3095271.

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Thesis (Ph. D.)--University of Oregon, 2003.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 69-71). Also available for download via the World Wide Web; free to University of Oregon users.

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Larsson, Christian. « Application development for automated positioning of 3D-representations of a modularized product ». Thesis, Linköpings universitet, Programvara och system, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-95466.

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This thesis presents an application that performs positioning of modules automatically based on given data for every module, and the development of it. The basis of the application is from a previous thesis code. On top of that code, more features and error handling has been added, as well as fixes for various bugs. A stress test has been performed and further development possibilities are being presented. The thesis work was carried out at Toyota Material Handling Mjölby (TMH) and was made in parallel with another thesis by Fredrik Holden who was generating data for the application. For a complete understanding of the theory and background, please also read Holden’s thesis report “Development of method for automated positioning of 3D-representations of a modularized product”, as well as the former thesis ”Analysis for Automated Positioning of 3D-representation of a Modularized product””.
Detta examensarbete presenterar en applikation som positionerar moduler automatiskt med hjälp av given data för varje modul, samt utvecklingen av applikationen. Applikationen bygger på kod från ett tidigare examensarbete. Ovanpå den koden har flera egenskaper och felhanteringar lagts till, samt har olika buggar fixats. Ett stresstest har också utförts och framtida utvecklingsmöjligheter presenteras. Examensarbetet genomfördes på Toyota Material Handling Mjölby (TMH) och gjordes parallellt med ett annat examensarbete av Fredrik Holden som genererade data för applikationen. För en fullständig förståelse angående teorin bakom samt bakgrunden till examensarbetet, vänligen läs också Holdens rapport ”Developmentof method for automated positioning of 3D-representations of a modularized product”, samt rapporten från föregeånde examensarbetet ”Analysis for Automated Positioning of 3D-representation of a Modularized product”.

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37

Taixés, Ventosa Xavier. « Theoretical and algorithmic aspects of congruences between modular Galois representations ». kostenfrei, 2009. http://duepublico.uni-duisburg-essen.de/servlets/DocumentServlet?id=20515.

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38

Williams, Adrian Leonard. « Some more decomposition numbers for modular representations of symmetric groups ». Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313541.

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39

Low, Gordan MacLaren. « Injective modules and representational repleteness ». Thesis, University of Glasgow, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319776.

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40

Baland, Shawn. « Some results on modules of constant Jordan type for elementary abelian-ρ-group ». Thesis, University of Aberdeen, 2012. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=192251.

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Let E be an elementary abelian p-group of rank r and k an algebraically closed field of characteristic p. We investigate finitely generated kE-modules of stable constant Jordan type [a][b] with 1 ≤ a, b ≤ p − 1 using the functors Fi from finitely generated kE-modules to vector bundles on the projective space Pr−1 constructed by Benson and Pevtsova. In particular, we study relations on the Chern numbers of the trivial bundle M to obtain restrictions on a and b for sufficiently large ranks and primes. We then study kE-modules with the constant image property and define the constant image layers of a module with respect to its maximal submodule having the constant image property. We prove that almost all such subquotients are semisimple. Focusing on the class of W-modules in rank two, we also calculate the vector bundles Fi(M) for all W-modules M. For E of rank two, we derive a duality formula for kE-modules M of constant Jordan type and their generic kernels K(M). We use this to answer a question of Carlson, Friedlander and Suslin regarding whether or not the submodules J−iK(M) also have constant Jordan type for all i ≥ 0. We show that this question has an affirmative answer whenever p = 3 or J2K(M) = 0. We also show that it has a negative answer in general by constructing a kE-module M of constant Jordan type for p ≥ 5 such that J−1K(M) does not have constant Jordan type. Finally, we use ideas from a theorem of Benson to show that if M is a kE-module of constant Jordan type containing no Jordan blocks of length one, then there always exist submodules of J−1K(M)/J2K(M) having a particularly nice structure.

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41

Amorós, Carafí Laia. « Images of Galois representations and p-adic models of Shimura curves ». Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/471452.

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The Langlands program is a vast and unifying network of conjectures that connect the world of automorphic representations of reductive algebraic groups and the world of Galois representations. These conjectures associate an automorphic representation of a reductive algebraic group to every n-dimensional representation of a Galois group, and the other way around: they attach a Galois representation to any automorphic representation of a reductive algebraic group. Moreover, these correspondences are done in such a way that the automorphic L-functions attached to the two objects coincide. The theory of modular forms is a field of complex analysis whose main importance lies on its connections and applications to number theory. We will make use, on the one hand, of the arithmetic properties of modular forms to study certain Galois representations and their number theoretic meaning. On the other hand, we will use the geometric meaning of these complex analytic functions to study a natural generalization of modular curves. A modular curve is a geometric object that parametrizes isomorphism classes of elliptic curves together with some additional structure depending on some modular subgroup. The generalization that we will be interested in are the so called Shimura curves. We will be particularly interested in their p-adic models. In this thesis, we treat two different topics, one in each side of the Langlands program. In the Galois representations' side, we are interested in Galois representations that take values in local Hecke algebras attached to modular forms over finite fields. In the automorphic forms' side, we are interested in Shimura curves: we develop some arithmetic results in definite quaternion algebras and give some results about Mumford curves covering p-adic Shimura curves.

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42

Citro, Craig Louis. « L-invariants of adjoint square Galois representations coming from modular forms ». Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872905031&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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43

Cui, Peiyi. « Modulo l-representations of p-adic groups SL_n(F) ». Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S050/document.

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Fixons un nombre premier p. Soit k un corps algébriquement clos de caractéristique l différent que p. Nous construisons les k-types maximaux simples cuspidaux des sous-groupes de Levi M' de SL_n(F), où F est un corps local non archimédien de caractéristique résiduelle p. Nous montrons que le support supercuspidal des k-représentations lisses irréductibles de M' est unique à M'-conjugaison près, quand F est soit un corps fini de caractéristique p soit un corps local non-archimédien de caractéristique résiduelle p
Fix a prime number p. Let k be an algebraically closed field of characteristic l different than p. We construct maximal simple cuspidal k-types of Levi subgroups M' of SL_n(F), where F is a non-archimedean locally compact field of residual characteristic p. And we show that the supercuspidal support of irreducible smooth k-representations of Levi subgroups M' of SL_n(F) is unique up to M'-conjugation, when F is either a finite field of characteristic p or a non-archimedean locally compact field of residual characteristic p

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44

Vienney, Mathieu. « Construction de (phi,gamma)-modules en caractéristique p ». Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00763785.

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Cette thèse est constituée de deux parties indépendantes, étudiant deux aspects de la théorie des (φ,Γ)-modules en caractéristique p. La première partie porte sur l'étude de la réduction modulo p des représentations cristallines irréductibles de dimension deux. Nous donnons, pour des poids k ≤ p², un calcul explicite de la réduction de V(k,a) pour a dans un disque fermé centré en zéro, généralisant ainsi des résultats déjà connus pour k ≤ 2p. En particulier, nous calculons le plus grand rayon possible pour ce disque, et montrons que dans certains cas, la réduction qui est constante à l'intérieur du disque change sur son bord. Dans la seconde partie, nous nous intéressons aux représentations d'un sous-groupe de Borel de GL[indice]2(Q[indice]p) sur un corps de caractéristique p, et en particulier à celles qui sont lisses, irréductibles et admettent un caractère central. Une méthode pour construire de telles représentations à partir de (φ,Γ)-modules irréductibles a été décrite par Colmez dans sa construction de la correspondance de Langlands p-adique. Après avoir donné un cadre un peu plus général dans lequel la construction de Colmez fonctionne encore, nous classifions les représentations irréductibles du Borel, prouvant que la construction précédente permet d'obtenir toutes les représentations de dimension infinie. Lorsque le corps des coefficients est fini, ou algébriquement clos, nous disposons d'une interprétation galoisienne des (φ,Γ)-modules irréductibles, et la classification précédente permet alors d'obtenir une correspondance entre ces représentations du Borel et des représentations galoisiennes modulaires.

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45

Forrester-Barker, Magnus. « Representations of crossed modules and catÂ¹-groups ». Thesis, Bangor University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401882.

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46

Kurinczuk, Robert James. « Smooth ℓ-modular representations of unramified p-ADIC U(2,1)(E/F) ». Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/41947/.

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Let E/F be an unramified quadratic extension of p-adic fields and G be the unitary group U(2,1)(E/F). In this thesis we construct all ℓ-modular irreducible cuspidal representations of G by compact induction from irreducible representations of compact open subgroups of G. Under an assumption on the possible cuspidal subquotients of representations parabolically induced from an irreducible positive level representation, we show that the supercuspidal support of an irreducible ℓ-modular representation of G is unique up to conjugacy.

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47

Steinberg, David. « Homological Properties of Standard KLR Modules ». Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22292.

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Khovanov-Lauda-Rouquier algebras, or KLR algebras, are a family of algebras known to categorify the upper half of the quantized enveloping algebra of a given Lie algebra. In finite type, these algebras come with a family of standard modules, which correspond to PBW bases under this categorification. In this thesis, we show that there are no non-zero homomorphisms between distinct standard modules and that all non-zero endomorphisms of standard modules are injective. We then apply this result to obtain applications to the modular representation theory of KLR algebras. Restricting our attention to finite type A, we are then able to compute explicit projective resolutions of all standard modules. Finally, in finite type A when alpha is a positive root, we let D be the direct sum of all distinct standard modules and compute the algebra structure on Ext(D, D). This dissertation includes unpublished co-authored material.

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48

Lacabanne, Abel. « Catégorification de données Z-modulaires et groupes de réflexions complexes ». Thesis, Montpellier, 2018. http://www.theses.fr/2018MONTS045/document.

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Cette thèse porte sur l'étude des données $mathbb{Z}$-modulaires et leur catégorification, et particulièrement sur des données $mathbb{Z}$-modulaires reliées aux groupes de réflexions complexes, ainsi que sur la notion de caractère cellulaire pour ces derniers. Dans sa classification des caractères des groupes finis de type de Lie, Lusztig décrit une transformée de Fourier non abélienne et définit des données $mathbb{N}$-modulaires pour chaque famille de caractères unipotents. Dans des tentatives de généralisation aux Spetses, Broué, Malle et Michel introduisent des données $mathbb{Z}$-modulaires. On commence par donner une explication catégorique de certaines de ces données via la catégorie des représentations du double de Drinfeld d'un groupe fini, que l'on munit d'une structure pivotale non sphérique. Une étude approfondie de la notion de catégorie de fusion pivotale et légèrement dégénérée montre que l'on peut ainsi produire des données $mathbb{Z}$-modulaires. Afin de construire des exemples de telles catégories, on considère des extensions des catégories de fusion associées à $qgrroot{mathfrak{g}}$, où $mathfrak{g}$ est une algèbre de Lie simple, et $xi$ une racine de l'unité. Ces dernières sont construites comme des semi-simplifications de la catégorie des modules basculants de l'algèbre $qdblroot{mathfrak{g}}$, qui est une extension centrale de $qgrroot{mathfrak{g}}$. Dans le cas où $mathfrak{g}=mathfrak{sl}_{n+1}$, on relie cette catégorie à une des données $mathbb{Z}$-modulaires associée au groupe de réflexions complexes $Gleft(d,1,frac{n(n+1)}{2}right)$. Les groupes de réflexions exceptionnels sont également étudiés, et les catégorifications des données $mathbb{Z}$-modulaires associées font apparaître diverses catégories : des catégories de représentations de doubles de Drinfeld tordus ainsi que des sous-catégories des catégories de fusion des modules basculants en $qdblroot{mathfrak{g}}$ en type $A$ et $B$
This work is a contribution to the categorification of $mathbb{Z}$-modular data and deals mainly with $mathbb{Z}$-modular data arising from complex reflection groups, as well as cellular characters for these groups. In his classification of representations of finite groups of Lie type, Lusztig defines a nonabelian Fourier transform, and associate a $mathbb{N}$-modular datum to each family of unipotent characters. In a generalization of Lusztig's theory to Spetses, Broué, Malle and Michel construct $mathbb{Z}$-modular data associated to some complex reflection groups. We first give a categorical explanation of some of these $mathbb{Z}$-modular data in terms of representation of the Drinfeld double of a finite group. We had to endow the category of representations with a non-spherical structure. The study of slightly degenerate categories shows that they naturally give rise to $mathbb{Z}$-modular data. In order to construct some examples, we consider an extension of the fusion categories associated to $qgrroot{mathfrak{g}}$, where $mathfrak{g}$ is a simple Lie algebra and $xi$ a root of unity. These categories are constructed as semisimplification of the category of tilting modules of $qdblroot{mathfrak{g}}$, which is a central extension of $qgrroot{mathfrak{g}}$. If $mathfrak{s}=mathfrak{sl}_{n+1}$, we show that this category is related to some $mathbb{Z}$-modular data associated to the complex reflection group $Gleft(d,1,frac{n(n+1)}{2}right)$. Exceptional complex reflection groups are also considered and many different categories appear in the categorification of the associated $mathbb{Z}$-modular data : modules categories over twisted Drinfeld doubles as well as some subcategories of fusion categories of tilting modules over $qdblroot{mathfrak{g}}$ in type $A$ and $B$

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49

Ruff, Oliver. « Completely splittable representations of symmetric groups and affine Hecke algebras / ». view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190545.

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Thesis (Ph. D.)--University of Oregon, 2005.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

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50

Wang, Erickson Carl William. « Moduli of Galois Representations ». Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10933.

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The theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The central object of study is the geometry of the map $\bar{\psi}$ from the moduli stack of representations to the moduli scheme of pseudorepresentations. The first chapter culminates in showing that $\bar{\psi}$ is very close to an adequate moduli space of Alper. In particular, $\bar{\psi}$ is universally closed. The second chapter refines the results of the first chapter. In particular, certain projective subschemes of the fibers of $\bar{\psi}$ are identified, generalizing a suggestion of Kisin. The third chapter applies the results of the first two chapters to moduli groupoids of continuous representations and pseudorepresentations of profinite algebras. In this context, the moduli formal scheme of pseudorepresentations is semi-local, with each component Spf $B_\bar{D}$ being the moduli of deformations of a given finite field-valued pseudorepresentation $\bar{D}$. Under a finiteness condition, it is shown that $\bar{\psi}$ is not only formally finite type over Spf $B_\bar{D}$, but arises as the completion of a finite type algebraic stack over Spec $B_\bar{D}$. Finally, the fourth chapter extends Kisin's construction of loci of coefficient spaces for p-adic local Galois representations cut out by conditions from p-adic Hodge theory. The result is extended from the case that the coefficient ring is a complete Noetherian local ring to the more general case that the coefficient space is a Noetherian formal scheme.
Mathematics

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Thèses sur le sujet « Modular representation »

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