Journal articles: 'Representations of groups'

1

Jakubík, Ján, and Gabriela Pringerová. "Representations of cyclically ordered groups." Časopis pro pěstování matematiky 113, no. 2 (1988): 184–96. http://dx.doi.org/10.21136/cpm.1988.118342.

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2

ZHENG, H. "A REFLEXIVE REPRESENTATION OF BRAID GROUPS." Journal of Knot Theory and Its Ramifications 14, no. 04 (June 2005): 467–77. http://dx.doi.org/10.1142/s0218216505003877.

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In this paper, for every positive integer m, we define a representation ξn,m of the n-strand braid group Bn over a free ℤBn+m-module. It not only provides an approach to construct new representations of braid groups, but also gives a new perspective to the homological representations such as the Lawrence–Krammer representation.

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3

Milnes, Paul. "Representations of Compact Right Topological Groups." Canadian Mathematical Bulletin 36, no. 3 (September 1, 1993): 314–23. http://dx.doi.org/10.4153/cmb-1993-044-1.

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AbstractCompact right topological groups arise naturally as the enveloping semigroups of distal flows. Recently, John Pym and the author established the existence of Haar measure μ on such groups, which invites the consideration of the regular representations. We start here by characterizing the continuous representations of a compact right topological group G, and are led to the conclusion that the right regular representation r is not continuous (unless G is topological). The domain of the left regular representation l is generally taken to be the topological centreor a tractable subgroup of it, furnished with a topology stronger than the relative topology from G (the goals being to have l both defined and continuous). An analysis of l and r on H = L2(G) for some non-topological compact right topological groups G shows, among other things, that: (i)for the simplest (perhaps) G generated by ℤ, (l, H) decomposes into one copy of each irreducible representation of ℤ and c copies of the regular representation.(ii)for the simplest (perhaps) G generated by the euclidean group of the plane , (l, H) decomposes into one copy of each of the continuous one-dimensional representations of and c copies of each continuous irreducible representation Ua,a > 0.(iii)when Λ(G) is not dense in G, it can seem very reasonable to regard r as a continuous representation of a related compact topological group, and also, G can be almost completely "lost" in the measure space (G, μ).

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BIGELOW, STEPHEN, and JIANJUN PAUL TIAN. "GENERALIZED LONG-MOODY REPRESENTATIONS OF BRAID GROUPS." Communications in Contemporary Mathematics 10, supp01 (November 2008): 1093–102. http://dx.doi.org/10.1142/s0219199708003186.

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Long and Moody give a method of constructing representations of the braid groups Bn. We discuss some ways to generalize their construction. One of these gives representations of subgroups of Bn, including the Gassner representation of the pure braid group as a special case. Another gives representations of the Hecke algebra.

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EGEA, CLAUDIA MARÍA, and ESTHER GALINA. "SELF-ADJOINT REPRESENTATIONS OF BRAID GROUPS." Journal of Knot Theory and Its Ramifications 21, no. 03 (March 2012): 1250009. http://dx.doi.org/10.1142/s0218216511009819.

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We give a method to construct new self-adjoint representations of 𝔹n of finite dimension. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient condition for a representation to be constructed with this method.

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LIVINGSTON, CHARLES. "LIFTING REPRESENTATIONS OF KNOT GROUPS." Journal of Knot Theory and Its Ramifications 04, no. 02 (June 1995): 225–34. http://dx.doi.org/10.1142/s0218216595000120.

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Given a representation of a classical knot group onto a quotient group E/A, we address the classification of lifts of that representation onto E. The classification is given first in terms of classical obstruction theory and then, in many cases, interpreted in terms of the homology of covers of the knot complement. Applications include the study of dihedral, metacyclic, and metabelian representations. Properties of the restrictions of lifts to the peripheral subgroup are also studied.

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7

Zhou, Jian. "Representation Rings of Classical Groups and Hopf Algebras." International Journal of Mathematics 14, no. 05 (July 2003): 461–77. http://dx.doi.org/10.1142/s0129167x03001922.

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We prove a double coset formula for induced representations of compact Lie groups. We apply it to the representation rings of unitary and symplectic groups to obtain Hopf algebras. We also construct a Heisenberg algebra representation based on the restiction and induction of representations of unitary groups.

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8

Wagner, Wolfgang, and Maaris Raudsepp. "Representations in Intergroup Relations: Reflexivity, Meta-Representations, and Interobjectivity." RUDN Journal of Psychology and Pedagogics 18, no. 2 (December 15, 2021): 332–45. http://dx.doi.org/10.22363/2313-1683-2021-18-2-332-345.

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Social and cultural groups are characterised by shared systems of social objects and issues that constitute their objective reality and their members' identity. It is argued that interpersonal interactions within such groups require a system of comprehensive representations to enable concerted interaction between individuals. Comprehensive representations include bits and pieces of the interactant's representational constitution and potential values and behaviours to reduce possible friction in interactions. On a larger scale, the same is true in encounters, communication, and interaction between members of different cultural groups where interactants need to dispose of a rough knowledge of the other culture's relevant characteristics. This mutual knowledge is called meta-representations that complement the actors' own values and ways of thinking. This concept complements Social Representation Theory when applied to cross-cultural and inter-ethnic interactions.

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9

Scevenels, Dirk. "On decomposable pseudofree groups." International Journal of Mathematics and Mathematical Sciences 22, no. 3 (1999): 617–28. http://dx.doi.org/10.1155/s0161171299226178.

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An Abelian group is pseudofree of rankℓif it belongs to the extended genus ofℤℓ, i.e., its localization at every primepis isomorphic toℤpℓ. A pseudofree group can be studied through a sequence of rational matrices, the so-called sequential representation. Here, we use these sequential representations to study the relation between the product of extended genera of free Abelian groups and the extended genus of their direct sum. In particular, using sequential representations, we give a new proof of a result by Baer, stating that two direct sum decompositions into rank one groups of a completely decomposable pseudofree Abelian group are necessarily equivalent. On the other hand, sequential representations can also be used to exhibit examples of pseudofree groups having nonequivalent direct sum decompositions into indecomposable groups. However, since this cannot occur when using the notion of near-isomorphism rather than isomorphism, we conclude our work by giving a characterization of near-isomorphism for pseudofree groups in terms of their sequential representations.

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10

DE JEU, MARCEL, and MARTEN WORTEL. "POSITIVE REPRESENTATIONS OF FINITE GROUPS IN RIESZ SPACES." International Journal of Mathematics 23, no. 07 (June 27, 2012): 1250076. http://dx.doi.org/10.1142/s0129167x12500760.

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In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite-dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite-dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive G-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.

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11

Kieou, Essoyomewè, Mawoussi Todjro, and Yaogan Mensah. "Rough representations of rough topological groups." Applied General Topology 24, no. 2 (October 2, 2023): 333–41. http://dx.doi.org/10.4995/agt.2023.18577.

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12

Kozma, Gady, and Alexander Lubotzky. "Linear representations of random groups." Bulletin of Mathematical Sciences 09, no. 03 (December 2019): 1950016. http://dx.doi.org/10.1142/s1664360719500164.

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We show that for a fixed [Formula: see text], Gromov random groups with any density [Formula: see text] have no nontrivial degree [Formula: see text] representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when [Formula: see text] such groups have a faithful linear representation over [Formula: see text], a.a.s.

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13

Bardakov, Valeriy G., Yuliya A. Mikhalchishina, and Mikhail V. Neshchadim. "Representations of virtual braids by automorphisms and virtual knot groups." Journal of Knot Theory and Its Ramifications 26, no. 01 (January 2017): 1750003. http://dx.doi.org/10.1142/s0218216517500031.

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In the present paper, a new representation of the virtual braid group [Formula: see text] into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for [Formula: see text] is verified. Using representations of [Formula: see text], a virtual link group is defined. Also representations of the welded braid group [Formula: see text] are constructed and the welded link group is defined.

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14

Valverde, Cesar. "On Induced Representations Distinguished by Orthogonal Groups." Canadian Mathematical Bulletin 56, no. 3 (September 1, 2013): 647–58. http://dx.doi.org/10.4153/cmb-2012-008-0.

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Abstract.LetFbe a local non-archimedean field of characteristic zero. We prove that a representation ofGL(n,F) obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.

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15

Banica, Teodor, and Alexandru Chirvasitu. "Quasi-flat representations of uniform groups and quantum groups." Journal of Algebra and Its Applications 18, no. 08 (July 5, 2019): 1950155. http://dx.doi.org/10.1142/s021949881950155x.

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Given a discrete group [Formula: see text] and a number [Formula: see text], a unitary representation [Formula: see text] is called quasi-flat when the eigenvalues of each [Formula: see text] are uniformly distributed among the [Formula: see text]th roots of unity. The quasi-flat representations of [Formula: see text] form altogether a parametric matrix model [Formula: see text]. We compute here the universal model space [Formula: see text] for various classes of discrete groups, notably with results in the case where [Formula: see text] is metabelian. We are particularly interested in the case where [Formula: see text] is a union of compact homogeneous spaces, and where the induced representation [Formula: see text] is stationary in the sense that it commutes with the Haar functionals. We present several positive and negative results on this subject. We also discuss similar questions for the discrete quantum groups, proving a stationarity result for the discrete dual of the twisted orthogonal group [Formula: see text].

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16

GRINBERG, DARIJ, JIA HUANG, and VICTOR REINER. "Critical groups for Hopf algebra modules." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 3 (November 7, 2018): 473–503. http://dx.doi.org/10.1017/s0305004118000786.

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AbstractThis paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations studied in [1, 11]. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable projective representations.

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17

Valette, Alain. "Representations of minimally almost periodic groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (December 1986): 366–75. http://dx.doi.org/10.1017/s1446788700033838.

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AbstractFor any groupG, we introduce the subsetS(G) of elementsgwhich are conjugate tofor some positive integerk. We show that, for any bounded representation π ofGanyginS(G), either π(g) = 1 or the spectrum of π(g) is the full unit circle in C. As a corollary,S(G) is in the kernel of any homomorphism fromGto the unitary group of a post-liminalC*-algebra with finite composition series.Next, for a topological groupG, we consider the subset of elements approximately conjugate to 1, and we prove that it is contained in the kernel of any uniformly continuous bounded representation ofG, and of any strongly continuous unitary representation in a finite von Neumann algebra.We apply these results to prove triviality for a number of representations of isotropic simple algebraic groups defined over various fields.

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18

Dong, Junbin. "Alvis–Curtis duality for representations of reductive groups with Frobenius maps." Forum Mathematicum 32, no. 5 (September 1, 2020): 1289–96. http://dx.doi.org/10.1515/forum-2020-0053.

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AbstractWe generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

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19

Aniello, P., C. Lupo, and M. Napolitano. "Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices." Open Systems & Information Dynamics 13, no. 04 (December 2006): 415–26. http://dx.doi.org/10.1007/s11080-006-9023-1.

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In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U (N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

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20

Lord, Nick, and Ernest B. Vinberg. "Linear Representations of Groups." Mathematical Gazette 74, no. 468 (June 1990): 199. http://dx.doi.org/10.2307/3619407.

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21

Chuang, Joseph, Markus Linckelmann, Gunter Malle, and Jeremy Rickard. "Representations of Finite Groups." Oberwolfach Reports 9, no. 1 (2012): 963–1019. http://dx.doi.org/10.4171/owr/2012/16.

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22

Chuang, Joseph, Meinolf Geck, Markus Linckelmann, and Gabriel Navarro. "Representations of Finite Groups." Oberwolfach Reports 12, no. 2 (2015): 971–1027. http://dx.doi.org/10.4171/owr/2015/18.

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23

Chuang, Joseph, Meinolf Geck, Radha Kessar, and Gabriel Navarro. "Representations of Finite Groups." Oberwolfach Reports 16, no. 1 (February 26, 2020): 841–95. http://dx.doi.org/10.4171/owr/2019/14.

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24

Hasić, Amor. "Representations of Lie Groups." Advances in Linear Algebra & Matrix Theory 11, no. 04 (2021): 117–34. http://dx.doi.org/10.4236/alamt.2021.114009.

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25

Andersen, H. H. "REPRESENTATIONS OF ALGEBRAIC GROUPS." Bulletin of the London Mathematical Society 20, no. 6 (November 1988): 629–30. http://dx.doi.org/10.1112/blms/20.6.629.

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26

Green, J. A. "REPRESENTATIONS OF FINITE GROUPS." Bulletin of the London Mathematical Society 23, no. 1 (January 1991): 90–91. http://dx.doi.org/10.1112/blms/23.1.90.

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27

Vinárek, Jiří. "Simultaneous representations of groups." Discrete Mathematics 108, no. 1-3 (October 1992): 211–16. http://dx.doi.org/10.1016/0012-365x(92)90676-7.

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28

Kostrikin, A. I., and I. A. Chubarov. "Representations of finite groups." Journal of Soviet Mathematics 40, no. 3 (February 1988): 331–83. http://dx.doi.org/10.1007/bf01092892.

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29

Giansiracusa, Noah, and Jacob Manaker. "Matroidal representations of groups." Advances in Mathematics 366 (June 2020): 107089. http://dx.doi.org/10.1016/j.aim.2020.107089.

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30

Szechtman, Fernando, Allen Herman, and Mohammad A. Izadi. "Representations of McLain groups." Journal of Algebra 474 (March 2017): 288–328. http://dx.doi.org/10.1016/j.jalgebra.2016.10.035.

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Dudas, Olivier, Meinolf Geck, Radha Kessar, and Gabriel Navarro. "Representations of Finite Groups." Oberwolfach Reports 20, no. 2 (December 21, 2023): 1031–84. http://dx.doi.org/10.4171/owr/2023/19.

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32

Spinaci, Marco. "Rigidity of maximal holomorphic representations of Kähler groups." International Journal of Mathematics 26, no. 14 (December 2015): 1550113. http://dx.doi.org/10.1142/s0129167x1550113x.

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We investigate representations of Kähler groups [Formula: see text] to a semisimple non-compact Hermitian Lie group [Formula: see text] that are deformable to a representation admitting an (anti)-holomorphic equivariant map. Such representations obey a Milnor–Wood inequality similar to those found by Burger–Iozzi and Koziarz–Maubon. Thanks to the study of the case of equality in Royden’s version of the Ahlfors–Schwarz lemma, we can completely describe the case of maximal holomorphic representations. If [Formula: see text], these appear if and only if [Formula: see text] is a ball quotient, and essentially reduce to the diagonal embedding [Formula: see text]. If [Formula: see text] is a Riemann surface, most representations are deformable to a holomorphic one. In that case, we give a complete classification of the maximal holomorphic representations, which thus appear as preferred elements of the respective maximal connected components.

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33

Bigelow, Stephen J. "Bowling ball representations of braid groups." Journal of Knot Theory and Its Ramifications 27, no. 05 (April 2018): 1850035. http://dx.doi.org/10.1142/s0218216518500359.

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In a remark in his seminal 1987 paper, Jones describes a way to define the Burau matrix of a positive braid using a metaphor of bowling a ball down a bowling alley with braided lanes. We extend this definition to allow multiple bowling balls to be bowled simultaneously. We obtain representations of the Iwahori–Hecke algebra and a cabled version of the Temperley–Lieb representation.

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34

Raghuram, A. "A Künneth Theorem for p-Adic Groups." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 440–46. http://dx.doi.org/10.4153/cmb-2007-043-5.

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AbstractLet G1 and G2 be p-adic groups. We describe a decomposition of Ext-groups in the category of smooth representations of G1 × G2 in terms of Ext-groups for G1 and G2. We comment on for a supercuspidal representation π of a p-adic group G. We also consider an example of identifying the class, in a suitable Ext1, of a Jacquet module of certain representations of p-adic GL2n.

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35

Holzherr, A. K. "Groups with Finite Dimensional Irreducible Multiplier Representations." Canadian Journal of Mathematics 37, no. 4 (August 1, 1985): 635–43. http://dx.doi.org/10.4153/cjm-1985-033-2.

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Let G be a locally compact group and ω a normalized multiplier on G. Denote by V(G) (respectively by V(G, ω)) the von Neumann algebra generated by the regular representation (respectively co-regular representation) of G. Kaniuth [6] and Taylor [14] have characterized those G for which the maximal type I finite central projection in V(G) is non-zero (respectively the identity operator in V(G)).In this paper we determine necessary and sufficient conditions on G and ω such that the maximal type / finite central projection in V(G, ω) is non-zero (respectively the identity operator in V(G, ω)) and construct this projection explicitly as a convolution operator on L2(G). As a consequence we prove the following statements are equivalent,(i) V(G, ω) is type I finite,(ii) all irreducible multiplier representations of G are finite dimensional,(iii) Gω (the central extension of G) is a Moore group, that is all its irreducible (ordinary) representations are finite dimensional.

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Manuilov, V. M. "Almost-representations and asymptotic representations of discrete groups." Izvestiya: Mathematics 63, no. 5 (October 31, 1999): 995–1014. http://dx.doi.org/10.1070/im1999v063n05abeh000263.

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Bartel, Alex, and Tim Dokchitser. "Rational representations and permutation representations of finite groups." Mathematische Annalen 364, no. 1-2 (May 10, 2015): 539–58. http://dx.doi.org/10.1007/s00208-015-1223-y.

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ABDULRAHIM, MOHAMMAD N. "PURE BRAIDS AS AUTOMORPHISMS OF FREE GROUPS." Journal of Algebra and Its Applications 04, no. 04 (August 2005): 435–40. http://dx.doi.org/10.1142/s0219498805001277.

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We study the composition of F. R. Cohen's map Pn → Pnk with the Gassner representation, where Pn is the pure braid group. This gives us a linear representation of Pn whose composition factors are one copy of the Gassner representation of Pn and k - 1 copies of a diagonal representation, hence a direct sum of one-dimensional representations.

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Ban, Dubravka. "Jacquet Modules of Parabolically Induced Representations and Weyl Groups." Canadian Journal of Mathematics 53, no. 4 (August 1, 2001): 675–95. http://dx.doi.org/10.4153/cjm-2001-027-7.

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AbstractThe representation parabolically induced from an irreducible supercuspidal representation is considered. Irreducible components of Jacquet modules with respect to induction in stages are given. The results are used for consideration of generalized Steinberg representations.

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Gubanov, V. O., and L. N. Ovander. "Development of the Bethe Method for the Construction of Two-Valued Space Group Representations and Two-Valued Projective Representations of Point Groups." Ukrainian Journal of Physics 60, no. 9 (September 2015): 950–59. http://dx.doi.org/10.15407/ujpe60.09.0950.

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Aladova, E., and B. Plotkin. "PI-groups and PI-representations of groups." Journal of Mathematical Sciences 164, no. 2 (December 15, 2009): 155–62. http://dx.doi.org/10.1007/s10958-009-9745-z.

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Knappe, Henrike, and Oscar Schmidt. "Making Representations: The SDG Process and Major Groups’ Images of the Future." Global Environmental Politics 21, no. 2 (April 15, 2021): 23–43. http://dx.doi.org/10.1162/glep_a_00599.

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Abstract The Sustainable Development Goals (SDGs) process aimed to be more inclusive, transparent, and participatory than prior United Nations processes. This article traces the practices of representation that were performed by civil society actors during the SDG process. In doing so, we advance a performative approach in which the very process of making representation is examined. Its aim is to conceptualize and study representation as an aesthetic and political practice. This leads to the two central research questions of this article: How do civil society organizations in global environmental politics make representative claims by picturing their envisioned future? How are future representations (that is, the representation of futures or future beings) related to actor positions during the SDG process? Special emphasis is given to representations of “the future” as an ever-present frame of reference in environmental politics. Based on a systematic content analysis of the statements of two Major Groups—Children, and Youth and Farmers—we discuss the variety of future representations between the Major Groups and how especially more radical future representations are connected to rather precarious actor positions in representative claims.

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NEEB, KARL-HERMANN. "POSITIVE ENERGY REPRESENTATIONS AND CONTINUITY OF PROJECTIVE REPRESENTATIONS FOR GENERAL TOPOLOGICAL GROUPS." Glasgow Mathematical Journal 56, no. 2 (August 13, 2013): 295–316. http://dx.doi.org/10.1017/s0017089513000268.

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AbstractLetGandTbe topological groups, α :T→ Aut(G) a homomorphism defining a continuous action ofTonGandG♯:=G⋊αTthe corresponding semidirect product group. In this paper, we address several issues concerning irreducible continuous unitary representations (π♯,${\mathcal{H}}$) ofG♯whose restriction toGremains irreducible. First, we prove that, forT=${\mathbb R}$, this is the case for any irreducible positive energy representation ofG♯, i.e. for which the one-parameter groupUt:= π♯(1,t) has non-negative spectrum. The passage from irreducible unitary representations ofGto representations ofG♯requires that certain projective unitary representations are continuous. To facilitate this verification, we derive various effective criteria for the continuity of projective unitary representations. Based on results of Borchers forW*-dynamical systems, we also derive a characterization of the continuous positive definite functions onGthat extend toG♯.

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TANG, XIN, and YUNGE XU. "ON REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K,H))." Bulletin of the Australian Mathematical Society 78, no. 2 (October 2008): 261–84. http://dx.doi.org/10.1017/s0004972708000701.

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AbstractWe construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite-dimensional weight representation of Uq(fm(K,H)) is proved to be completely reducible. Finally, we study the Whittaker model for the center of Uq(fm(K,H)), and a classification of all irreducible Whittaker representations of Uq(fm(K,H)) is obtained.

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Savini, Alessio. "Rigidity at infinity for lattices in rank-one Lie groups." Journal of Topology and Analysis 12, no. 01 (August 29, 2018): 113–30. http://dx.doi.org/10.1142/s1793525319500420.

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Let [Formula: see text] be a non-uniform lattice in [Formula: see text] without torsion and with [Formula: see text]. By following the approach developed in [S. Francaviglia and B. Klaff, Maximal volume representations are Fuchsian, Geom. Dedicata 117 (2006) 111–124], we introduce the notion of volume for a representation [Formula: see text] where [Formula: see text]. We use this notion to generalize the Mostow–Prasad rigidity theorem. More precisely, we show that given a sequence of representations [Formula: see text] such that [Formula: see text], then there must exist a sequence of elements [Formula: see text] such that the representations [Formula: see text] converge to a reducible representation [Formula: see text] which preserves a totally geodesic copy of [Formula: see text] and whose [Formula: see text]-component is conjugated to the standard lattice embedding [Formula: see text]. Additionally, we show that the same definitions and results can be adapted when [Formula: see text] is a non-uniform lattice in [Formula: see text] without torsion and for representations [Formula: see text], still maintaining the hypothesis [Formula: see text].

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Arefaine, Nigusse, Kassa Michael, and Shimelis Assefa. "GeoGebra Assisted Multiple Representations for Enhancing Students’ Representation Translation Abilities in Calculus." Asian Journal of Education and Training 8, no. 4 (November 28, 2022): 121–30. http://dx.doi.org/10.20448/edu.v8i4.4309.

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Multiple representations cultivate students’ mathematical mindset. However, research results have reported that students do not benefit from these tools due to lack of representational fluency. This study was designed to determine the impact of GeoGebra assisted multiple representations approach on students’ representation translation performance in calculus. Pretest - posttest quasi experimental design was implemented. Three intact groups of first year first semester of social science students in the 2019/2020 academic year of size 53, 57 and 54 at Jigjiga and Kebri-Dehar Universities in Ethiopia were considered. The groups were taught with GeoGebra supported multiple representations (MRT), multiple representations (MR) and comparison group (CG). Representation translation test was given before and after the treatment. Furthermore, students’ translation errors were categorized as implementation, interpretation and preservation errors and analyzed using frequency and percentage. The ANCOVA result revealed that significant difference was obtained on the adjusted mean of RTF posttest (F (2,160) = 5.29, P = 0.006, Partial η2 =0.062) in favor of the MRT. The interpretation error was the most frequently committed among the groups. Recommendations were forwarded that included the use of GeoGebra and the need to conduct further study with different participants to generalize to the entire population.

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Morris, Lawrence. "Tamely ramified supercuspidal representations of classical groups. II. Representation theory." Annales scientifiques de l'École normale supérieure 25, no. 3 (1992): 233–74. http://dx.doi.org/10.24033/asens.1649.

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Bellaïche, Joël, and Gaëtan Chenevier. "The sign of Galois representations attached to automorphic forms for unitary groups." Compositio Mathematica 147, no. 5 (July 27, 2011): 1337–52. http://dx.doi.org/10.1112/s0010437x11005264.

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AbstractLet K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a twist by a power of the cyclotomic character. Absolutely irreducible polarized representations of GK have a sign ±1, generalizing the fact that a self-dual absolutely irreducible representation is either symplectic or orthogonal. If Π is a regular algebraic, polarized, cuspidal automorphic representation of GLn(𝔸K), and if ρ is a p-adic Galois representation attached to Π, then ρ is polarized and we show that all of its polarized irreducible constituents have sign +1 . In particular, we determine the orthogonal/symplectic alternative for the Galois representations associated to the regular algebraic, essentially self-dual, cuspidal automorphic representations of GLn (𝔸F) when F is a totally real number field.

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HILDEN, HUGH M., MARÍA TERESA LOZANO, and JOSÉ MARÍA MONTESINOS-AMILIBIA. "ON REPRESENTATIONS OF 2-BRIDGE KNOT GROUPS IN QUATERNION ALGEBRAS." Journal of Knot Theory and Its Ramifications 20, no. 10 (October 2011): 1419–83. http://dx.doi.org/10.1142/s0218216511009224.

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Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as E3 (Euclidean 3-space), H3 (hyperbolic 3-space) and E2, 1 (Minkowski 3-space), using quaternion algebra theory, are studied. We study the different representations of a 2-generator group in which the generators are send to conjugate elements, by analyzing the points of an algebraic variety, that we call the variety of affine c-representations ofG. Each point in this variety corresponds to a representation in the unit group of a quaternion algebra and their affine deformations.

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Elst, A. F. M. Ter, and Derek W. Robinson. "Subelliptic operators on Lie groups: regularity." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 2 (October 1994): 179–229. http://dx.doi.org/10.1017/s1446788700037514.

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AbstractLet (ℋ,G, U) be a continuous representation of the Lie groupGby bounded operatorsg↦U(g)on the Banach space ℋ and let (ℋ,g, dU) denote the representation of the Lie algebragobtained by differentiation. Ifa1,…, ad′is a Lie algebra basis ofgandAi= dU(ai)then we examine elliptic regularity properties of the subelliptic operatorswhere (cij) is a real-valued strictly positive-definite matrix andc0, c1,…, cd′∈ C. We first introduce a family of Lipschitz subspaces ℋγ, γ > 0, of ℋ which interpolate between theCn-subspaces of the representation and for which the parameter γ is a continuous measure of differentiability. Secondly, we give a variety of characterizations of the spaces in terms of the semigroup generated by the closureofHand the group representation. Thirdly, for sufficiently large values of Rec0the fractional powers of the closure ofHare defined, and we prove that D()γ⊆γ′, for γ′ < 2γ/rwhereris the rank of the basis. Further we establish that 2γ/ris the optimal regularity value and it is attained for unitary representations or for the representations obtained by restrictingUto ℋγ. Many other regularity properties are obtained.

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Journal articles on the topic 'Representations of groups'

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