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Dissertations / Theses on the topic 'Hecke algebra'

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Published: 4 June 2021

Last updated: 20 February 2023

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1

Uhl, Christine. "Quantum Drinfeld Hecke Algebras." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc862764/.

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Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex reflection groups acting in arbitrary dimension. We also classify quantum Drinfeld Hecke algebras i

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2

Schmidt, Nicolas Alexander. "Generic pro-p Hecke algebras, the Hecke algebra of PGL(2, Z), and the cohomology of root data." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19724.

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Es wird die Theorie der generischen pro-$p$ Hecke-Algebren und ihrer Bernstein-Abbildungen entwickelt. Für eine Unterklasse diese Algebren, der \textit{affinen} pro-$p$ Hecke-Algebren wird ein Struktursatz bewiesen, nachdem diese Algebren unter anderem stets noethersch sind, wenn es der Koeffizientenring ist. Hilfsmittel ist dabei der Nachweis der Bernsteinrelationen, der in abstrakter Weise geführt wird und so die bestehende Theorie verallgemeinert. Ferner wird der top. Raum der Orientierungen einer Coxetergruppe eingeführt und im Falle der erweiterten modularen Gruppe $\operatorname{PGL}_

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3

Soriano, Solá Marcos. "Contributions to the integral representation theory of Iwahori-Hecke algebras." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9866651.

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4

Alharbi, Badr. "Representations of Hecke algebra of type A." Thesis, University of East Anglia, 2013. https://ueaeprints.uea.ac.uk/48674/.

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We give some new results about representations of the Hecke algebra HF,q(Sn) of type A. In the first part we define the decomposition numbers dλν to be the composition multiplicity of the irreducible module Dν in the Specht module Sλ. Then we compute the decomposition numbers dλν for all partitions of the form λ = (a, c, 1b) and ν 2–regular for the Hecke algebra HC,−1(Sn). In the second part, we give some examples of decomposable Specht modules for the Hecke algebra HC,−1(Sn). These modules are indexed by partitions of the form (a, 3, 1b), where a, b are even. Finally, we find a new family of

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5

Ratliff, Leah J. "The alternating hecke algebra and its representations." Connect to full text, 2007. http://hdl.handle.net/2123/1698.

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Thesis (Ph. D.)--School of Mathematics and Statistics, Faculty of Science, University of Sydney, 2007.<br>Title from title screen (viewed 13 January 2009). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliographical references. Also available in print form.

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6

Ratliff, Leah Jane. "The alternating Hecke algebra and its representations." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/1698.

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The alternating Hecke algebra is a q-analogue of the alternating subgroups of the finite Coxeter groups. Mitsuhashi has looked at the representation theory in the cases of the Coxeter groups of type A_n, and B_n, and here we provide a general approach that can be applied to any finite Coxeter group. We give various bases and a generating set for the alternating Hecke algebra. We then use Tits' deformation theorem to prove that, over a large enough field, the alternating Hecke algebra is isomorphic to the group algebra of the corresponding alternating Coxeter group. In particular, there is a b

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7

Ratliff, Leah Jane. "The alternating Hecke algebra and its representations." University of Sydney, 2007. http://hdl.handle.net/2123/1698.

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Doctor of Philosophy<br>The alternating Hecke algebra is a q-analogue of the alternating subgroups of the finite Coxeter groups. Mitsuhashi has looked at the representation theory in the cases of the Coxeter groups of type A_n, and B_n, and here we provide a general approach that can be applied to any finite Coxeter group. We give various bases and a generating set for the alternating Hecke algebra. We then use Tits' deformation theorem to prove that, over a large enough field, the alternating Hecke algebra is isomorphic to the group algebra of the corresponding alternating Coxeter group. In

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8

Parkinson, James William. "Buildings and Hecke Algebras." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/642.

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We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers a

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9

Parkinson, James William. "Buildings and Hecke Algebras." University of Sydney. Mathematics and Statistics, 2005. http://hdl.handle.net/2123/642.

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We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers a

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10

Kusilek, Jonathan. "On representations of affine Hecke algebras." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/12074.

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We introduce a C-algebra Ht corresponding to an affine Hecke algebra H and a central character t of H, and show that the irreducible representations of Ht are precisely the irreducible representations of H with central character t. For certain choices of t we give an explicit construction of a cellular basis of Ht in terms of elementary properties of t. We thus classify, and give a construction of, the irreducible representations of Ht. While the indexing sets appear similar to those given for calibrated representations, we obtain many representations which are not calibrated.

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11

Shaplin, Richard Martin III. "Spherical Elements in the Affine Yokonuma-Hecke Algebra." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/99307.

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In Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module.<br>Master of Science<br>The Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-

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12

Forsberg, Love. "Effective representations of Hecke-Kiselman monoids of type A." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-174648.

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13

Solleveld, Maarten Sander. "Periodic cyclic homology of affine Hecke algebras." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2007. http://dare.uva.nl/document/45002.

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14

Krawzik, Naomi. "Graded Hecke Algebras for the Symmetric Group in Positive Characteristic." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707315/.

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Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not the action of the group. Lusztig's algebras are all isomorphic to Drinfeld's algebras in the nonmodu

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15

Leclerc, Marc-Antoine. "The Hyperbolic Formal Affine Demazure Algebra." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35218.

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In this thesis, we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of formal Demazure lattices of a Kac-Moody root system and show that the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.

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16

Stoll, Friederike. "On the action of Ariki-Koike algebras on tensor space." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB12168104.

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17

Roberts, Jeremiah. "Complex and p-adic Hecke Algebra with Applications to SL(2)." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/theses/2754.

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We discuss two versions of the Hecke algebra of a locally profinite group G, one that is complex valued and one that is p-adic valued. We reproduce several results which are well known for the complex valued Hecke algebra for the p-adic valued Hecke algebra. Specifically we show the equivalence of smooth representations of G and smooth modules of the Hecke algebra of G. We specialize to the group G=GLn(F) for F an extension of Qp, and show that the spherical Hecke algebra of G is finitely generated, and exhibit its generators. This is a standard fact for the complex valued Hecke

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18

Spencer, Matthew. "The representation theory of Iwahori-Hecke algebras with unequal parameters." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8644.

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The Iwahori-Hecke algebras of finite Coxeter groups play an important role in many areas of mathematics. In this thesis we study the representation theory of the Iwahori-Hecke algebras of the Coxeter groups of type Bn and F4, in the unequal parameter case. We denote these algebras HQ and KQ respectively. This follows on from work done by Dipper, James, Murphy and Norton. We are interested in the Iwahori-Hecke algebras of type Bn and F4 since these are the only cases, apart from the dihedral groups, where the Coxeter generators lie in different conjugacy classes, and therefore the Iwahori-Hecke

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19

Liu, Wille. "Double affine Hecke algebra of general parameters : perverse sheaves and Knizhnik--Zamolodchikov functor." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7144.

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Le présent travail de thèse porte sur l'étude de la catégorie O des algèbres de Hecke doublement affines dégénérées (dDAHA) au point de vue de la théorie de Springer et celle des faisceaux pervers. Dans les premiers deux chapitres nous étudions de manière algébrique les dDAHA et leurs généralisations, algèbres de Hecke doubles carquois (QDHA). Nous introduisons le foncteur de Knizhnik--Zamolodchikov (KZ) pour les QDHA et démontrons qu'ils vérifient la propriété bicommutante dans chapitre 2. Les chapitres 3 et 4 sont consacrés à l'étude des faisceaux pervers sur les algèbres de Lie munies de gr

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20

Speyer, Liron. "Representation theory of Khovanov-Lauda-Rouquier algebras." Thesis, Queen Mary, University of London, 2015. http://qmro.qmul.ac.uk/xmlui/handle/123456789/9114.

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This thesis concerns representation theory of the symmetric groups and related algebras. In recent years, the study of the “quiver Hecke algebras”, constructed independently by Khovanov and Lauda and by Rouquier, has become extremely popular. In this thesis, our motivation for studying these graded algebras largely stems from a result of Brundan and Kleshchev – they proved that (over a field) the KLR algebras have cyclotomic quotients which are isomorphic to the Ariki–Koike algebras, which generalise the Hecke algebras of type A, and thus the group algebras of the symmetric groups. This has al

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21

Alhaddad, Shemsi I. "Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5235/.

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The Iwahori-Hecke algebras of Coxeter groups play a central role in the study of representations of semisimple Lie-type groups. An important tool is the combinatorial approach to representations of Iwahori-Hecke algebras introduced by Kazhdan and Lusztig in 1979. In this dissertation, I discuss a generalization of the Iwahori-Hecke algebra of the symmetric group that is instead based on the complex reflection group G(r,1,n). Using the analogues of Kazhdan and Lusztig's R-polynomials, I show that this algebra determines a partial order on G(r,1,n) that generalizes the Chevalley-Bruhat order on

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22

Lawrence, Ruth Jayne. "Homology representations of braid groups." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236125.

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23

Fan, C. Kenneth (Chenteh Kenneth). "A Hecke algebra quotient and properties of commutative elements of a Weyl group." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11578.

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24

Schmidt, Nicolas Alexander [Verfasser], Elmar Gutachter] Große-Klönne, Yuval Z. [Gutachter] [Flicker, and Ulrich [Gutachter] Görtz. "Generic pro-p Hecke algebras, the Hecke algebra of PGL(2, Z), and the cohomology of root data / Nicolas Alexander Schmidt ; Gutachter: Elmar Große-Klönne, Yuval Zvi Flicker, Ulrich Görtz." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1197159886/34.

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Schmidt, Nicolas Alexander Verfasser], Elmar [Gutachter] Große-Klönne, Yuval Z. [Gutachter] [Flicker, and Ulrich [Gutachter] Görtz. "Generic pro-p Hecke algebras, the Hecke algebra of PGL(2, Z), and the cohomology of root data / Nicolas Alexander Schmidt ; Gutachter: Elmar Große-Klönne, Yuval Zvi Flicker, Ulrich Görtz." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1197159886/34.

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26

Orellana, Rosa C. "The Hecke algebra of type B at roots of unity, Markov traces and subfactors /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9938595.

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27

Lin, Qiang Flach Matthias. "Bloch-Kato conjecture for the adjoint of H1(X0(N)) with integral Hecke algebra /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-11182003-084742.

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28

Schüler, Axel. "Klassifikation von bikovarianten Differentialkalkülen auf Quantengruppen." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-218907.

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Unter der Voraussetzung, dass q keine Einheitswurzel ist und dass die Differentiale duij der Fundamentalmatrix den Linksmodul der 1-Formen erzeugen, werden die bikovarianten Differentialkalküle auf den Quantengruppen SLq(N), Oq(N) und Spq(N) klassifiziert. Es wird gezeigt, dass es auf den Quantengruppen SLq(N), N ≥ 3, abgesehen von eindimensionalen Kalkülen und endlich vielen Werten von q genau 2N bikovariante Differentialkalküle gibt. Diese Kalküle haben die Dimension N². Für die Quantengruppen Oq(N) und Spq(N), N ≥ 3, gibt es unter den genannten Voraussetzungen bis auf endlich viele Werte vo

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29

Lipp, Johannes. "Representations of Hecke algebras of Weyl groups of type A and B." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9600259.

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30

Graber, John Eric. "Cellularity and Jones basic construction." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/292.

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This thesis establishes a framework for cellularity of algebras related to the Jones basic construction. The framework allows a uniform proof of cellularity of Brauer algebras, BMW algebras, walled Brauer algebras, partition algebras, and others. In this setting, the cellular bases are labeled by paths on certain branching diagrams rather than by tangles. Moreover, for this class of algebras, the cellular structures are compatible with restriction and induction of modules.

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31

Fujita, Ryo. "A geometric study of Dynkin quiver type quantum affine Schur-Weyl duality." Kyoto University, 2019. http://hdl.handle.net/2433/242573.

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32

Hebert, Auguste. "Études des masures et de leurs applications en arithmétique." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSES027/document.

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Les masures ont été introduites en 2008 par Gaussent et Rousseau afin d’étudier les groupes de Kac-Moody sur les corps locaux. Elles généralisent les immeubles de Bruhat-Tits. Dans cette thèse, j’étudie d’une part les propriétés des masures et d’autre part leurs applications en arithmétique et en théorie des représentations. Rousseau a donné une définition axiomatique des masures, inspirée par la définition de Tits des immeubles de Bruhat-Tits. Je propose une axiomatique plus simple et plus agréable à manipuler et je montre que mon axiomatique est équivalente à celle de Rousseau.Nous étudions

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33

Poulain, D'Andecy Loïc. "Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique." Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00748920.

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Une approche inductive est développée pour la théorie des représentations de la chaîne des algèbres de Hecke cyclotomiques de type G(m,1,n). Cette approche repose sur l'étude du spectre d'une famille commutative maximale, formée par les analogues des éléments de Jucys-Murphy. Les représentations irréductibles, paramétrées par les multi-partitions, sont construites avec l'aide d'une nouvelle algèbre associative, dont l'espace vectoriel sous-jacent est le produit tensoriel de l'algèbre de Hecke cyclotomique avec l'algèbre associative libre engendrée par les multi-tableaux standards. L'analogue d

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Martino, Marcelo Gonçalves de. "On the unramified spherical automorphic spectrum." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4017/document.

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Cette thèse a deux résultats d'analyse harmonique sur des groupes réductifs. Soit G connexe et défini sur un corps de nombres F, A les adèles et K un sous-groupe compact maximal de G(A). On a étudié la décomposition de l'espace des fonctions de carré intégrable sur le l'espace quotient G(F)\G(A)/K, en tant que module sur une algèbre de Hecke global. Des résultats similaires que ceux obtenus ici ont été établies par divers auteurs pour de nombreux cas particuliers. La caractéristique principale de la présente approche réside dans le fait qu'il est uniforme. Cette approche a été inspirée par des

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35

Laugerotte, Eric. "Combinatoire et calcul symbolique en théorie des représentations." Rouen, 1997. http://www.theses.fr/1997ROUES069.

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Ce mémoire concerne le traitement algorithmique des représentations matricielles. Les techniques y sont illustrées sur deux exemples, les algèbres de Hecke et les automates à multiplicités. Les algèbres de Hecke interviennent dans plusieurs domaines (dont l'algèbre ou la physique statistique) qui demandent de pouvoir y calculer efficacement. Ici sont rassemblés des algorithmes implémentés en Maple constituant la bibliothèque SHRI. Par l'action d'opérateurs de symétrisation sur des Q-Vandermonde, on détermine un système complet de représentations polynomiales. En calculant les polynômes minimau

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36

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. T

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Boys, Clinton. "Alternating quiver Hecke algebras." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12725.

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This thesis consists of a detailed study of alternating quiver Hecke algebras, which are alternating analogues of quiver Hecke algebras as defined by Khovanov-Lauda and Rouquier. The main theorem gives an isomorphism between alternating quiver Hecke algebras and alternating Hecke algebras, as introduced by Mitsuhashi, in the style of Brundan and Kleshchev, provided the quantum characteristic is odd. A proof is obtained by adapting recent methods of Hu and Mathas, which rely on seminormal forms and coefficient systems. A presentation for alternating quiver Hecke algebras by generators and relat

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Rostam, Salim. "Algèbres de Hecke carquois et généralisations d'algèbres d'Iwahori-Hecke." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLV063/document.

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Cette thèse est consacrée à l'étude des algèbres de Hecke carquois et de certaines généralisations des algèbres d'Iwahori-Hecke. Dans un premier temps, nous montrons deux résultats concernant les algèbres de Hecke carquois, dans le cas où le carquois possède plusieurs composantes connexes puis lorsqu'il possède un automorphisme d'ordre fini. Ensuite, nous rappelons un isomorphisme de Brundan-Kleshchev et Rouquier entre algèbres d'Ariki-Koike et certaines algèbres de Hecke carquois cyclotomiques. D'une part nous en déduisons qu'une équivalence de Morita importante bien connue entre algèbres d'A

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Gehles, Katrin Eva. "Properties of Cherednik algebras and graded Hecke algebras." Thesis, University of Glasgow, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433167.

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40

Borie, Nicolas. "Calcul des invariants de groupes de permutations par transformée de Fourier." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112294/document.

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Cette thèse porte sur trois problèmes en combinatoire algébrique effective et algorithmique.Les premières parties proposent une approche alternative aux bases de Gröbner pour le calcul des invariants secondaires des groupes de permutations, par évaluation en des points choisis de manière appropriée. Cette méthode permet de tirer parti des symétries du problème pour confiner les calculs dans un quotient de petite dimension, et ainsi d'obtenir un meilleur contrôle de la complexité algorithmique, en particulier pour les groupes de grande taille. L'étude théorique est illustrée par de nombreux ban

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Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.

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Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funkt

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42

Stoica, Emanuel (Emanuel I. ). "Unitary representations of rational Cherednik algebras and Hecke algebras." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64606.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 49-50).<br>We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in

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Neshitov, Alexander. "Motivic Decompositions and Hecke-Type Algebras." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35009.

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Let G be a split semisimple algebraic group over a field k. Our main objects of interest are twisted forms of projective homogeneous G-varieties. These varieties have been important objects of research in algebraic geometry since the 1960's. The theory of Chow motives and their decompositions is a powerful tool for studying twisted forms of projective homogeneous varieties. Motivic decompositions were discussed in the works of Rost, Karpenko, Merkurjev, Chernousov, Calmes, Petrov, Semenov, Zainoulline, Gille and other researchers. The main goal of the present thesis is to connect motivic dec

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Fakiolas, A. P. "Hecke algebras and the Lusztig isomorphism." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379611.

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45

Anderson, Michael R. "Hecke algebras associated to Weyl groups /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487842372897758.

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46

Nash, David A. 1982. "Graded representation theory of Hecke algebras." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10871.

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xii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm

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Kerschl, Alexander. "Simple modules of cyclotomic Hecke algebras." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/20683.

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Ariki showed that the simple modules of the cyclotomic Hecke algebra are labelled by Kleshchev multipartitions. Recently, Jacon gave an alternative recursive description of Uglov multipartitions, which can be thought of as a generalisation of Kleshchev multipartitions. In this thesis we extend Jacon's combinatorics and then give a non-recursive description of Kleshchev multipartitions. We then use these combinatorial tools in the framework of the diagramatic Cherednik algebras to give a complete classification of the simple modules coming from the Webster-Bowman "many cellular bases" indexed b

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Casbi, Elie. "Categorifications of cluster algebras and representations of quiver Hecke algebras." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7032.

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Cette thèse porte sur l’étude de diverses conséquences des résultats de catégorifications monoïdales d'algèbres amassées par les algèbres de Hecke carquois, établis dans les travaux de Kang-Kashiwara-Kim-Oh [69]. Nous nous intéresserons en particulier à trois aspects de cette théorie: en premier lieu celui de la combinatoire, puis de la géométrie polytopale, et enfin celui de la théorie des représentations géométrique. Nous étudierons tout d'abord certaines relations combinatoires entre objets de nature a priori différentes: d'une part, les g-vecteurs au sens de Fomin-Zelevinsky, et d'autre pa

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Oblomkov, Alexei. "Double affine Hecke algebras and noncommutative geometry." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/31165.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.<br>Includes bibliographical references (p. 93-96).<br>In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the center Z of H(t, 1), and H(t, 1)e is a Cohen-Macaulay eH(t, 1)e-module with the property H(t, 1) = EndeH(t,tl)(H(t, 1)e). This implies the classification of the finite

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Dave, Ojas. "Irreducible Modules for Yokonuma-Type Hecke Algebras." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc862800/.

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Yokonuma-type Hecke algebras are a class of Hecke algebras built from a Type A construction. In this thesis, I construct the irreducible representations for a class of generic Yokonuma-type Hecke algebras which specialize to group algebras of the complex reflection groups and to endomorphism rings of certain permutation characters of finite general linear groups.

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