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REPRESENTATION THEORY OF SYMMETRIC GROUPS AND RELATED HECKE ALGEBRAS
, 2009
"... Abstract. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition n ..."
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Abstract. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic
On Tensor Products Of Modular Representations Of Symmetric Groups
 BULL. LONDON MATH. SOC
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On Kronecker products of spin characters of the double covers of the symmetric groups
 PACIFIC J. MATH
, 2001
"... In this article,restrictions on the constituents of Kronecker products of spin characters of the double covers of the symmetric groups are derived. This is then used to classify homogeneous and irreducible products of spin characters; as an application of this,certain homogeneous 2modular tensor pr ..."
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In this article,restrictions on the constituents of Kronecker products of spin characters of the double covers of the symmetric groups are derived. This is then used to classify homogeneous and irreducible products of spin characters; as an application of this,certain homogeneous 2modular tensor products for the symmetric groups are described.
Irreducible tensor products of representations of finite quasisimple groups of Lie type
"... . Let G be a finite quasisimple group of Lie type defined over a field of characteristic p. We determine whether G can possess irreducible Brauer characters ff, fi (of degree ? 1) in characteristic other than p such that ff\Omega fi is irreducible. 1. Introduction Let G be a finite group, r a fixe ..."
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. Let G be a finite quasisimple group of Lie type defined over a field of characteristic p. We determine whether G can possess irreducible Brauer characters ff, fi (of degree ? 1) in characteristic other than p such that ff\Omega fi is irreducible. 1. Introduction Let G be a finite group, r a fixed prime (or r = 0). Consider the following statement P(r) : ff\Omega fi is not irreducible for any nonlinear Brauer characters ff; fi 2 IBr r (G) (by IBr r (G) with r = 0 we mean Irr(G)). One motivation for studying the property P(r) comes from the desire to classify the overgroups of the irreducible subgroups of the finite classical groups G(q). According to Aschbacher's Theorem [A], if M is a maximal subgroup of G(q), then either M belongs to one of 8 collections C i , 1 i 8, of "natural" subgroups of G(q), or M 2 S, a collection of quasisimple groups which act irreducibly on the natural module V of G(q). For instance, C 4 consists of stabilizers of tensor decompositions of V . Conv...
ON RESTRICTIONS OF MODULAR SPIN REPRESENTATIONS OF SYMMETRIC AND ALTERNATING GROUPS
, 2003
"... Let F be an algebraically closed field of characteristic p and H be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups G of H and FHmodules V such that the restriction V ↓ G is irreducible. For exampl ..."
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Let F be an algebraically closed field of characteristic p and H be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups G of H and FHmodules V such that the restriction V ↓ G is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where H is the Schur’s double cover Ân or ˆ Sn.
Right Type Departmental Bulletin Paper
"... Tensor products of representations of the symmetric groups and related groupsl ..."
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Tensor products of representations of the symmetric groups and related groupsl
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"... the structure of the tensor square of the natural module of the symmetric group ..."
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the structure of the tensor square of the natural module of the symmetric group