Projective representations of the generalized symmetric groups

Projective Representations of Generalized Symmetric Groups

Representations of the Generalized Symmetric Groups

The Howe Duality and the Projective Representations of Symmetric Groups

The symmetric group Sk possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of Sk itself, coincide with the irreducible representations of the algebra Ak generated by indeterminates τi,j for i 6= j, 1 ≤ i, j ≤ n subject to the relations τi,j = −τj,i, τ i,j = 1, τi,jτm,l = −τm,lτi,j if {i, j} ∩ {m, l} = ∅; τi,jτj,mτi,j = τj,m...

Representations of symmetric groups

In this thesis we study the ordinary and the modular representation theory of the symmetric group. In particular we focus our work on different important open questions in the area. 1. Foulkes’ Conjecture In Chapter 2 we focus our attention on the long standing open problem known as Foulkes’ Conjecture. We use methods from character theory of symmetric groups to determine new information on the...

Representations of Symmetric Groups

A surprising theorem in the modular representation theory of symmetric groups uses induction and restriction functors to define an action of an affine Kac-Moody special linear algebra on the level of Grothendieck groups. This action identifies the direct sum of Grothendieck groups with an integrable highest weight module of the Kac-Moody algebra. The purpose of this write-up is to provide a gen...