The projective representations: of the generalized symmetric group

Projective Representations of 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...

The Representations of the Symmetric Group

In this paper we classify the irreducible representations of the symmetric group Sn and give a proof of the hook formula for the dimension of each irreducible. 1. The Irreducible Representations of Sn We construct the irreducible representations of the symmetric group. The number of irreducible representations of Sn is the number of conjugacy classes of Sn, which is the number of partitions of ...

Representations of the Generalized Symmetric Groups

Irreducible Representations of the Symmetric Group

We construct the Specht modules and prove that they completely characterize the irreducible representations of the symmetric group. We will prove certain properties of these representations using combinatorial tools (such as calculating the dimension using Hook’s length formula). Only an introductory knowledge of group theory and linear algebra will be assumed and representation theory concepts...