On Kronecker products of complex representations of the symmetric and alternating groups

Abstract

In this paper we study the homogeneous tensor products of simple modules over symmetric and alternating groups.

On restrictions of modular spin representations of symmetric and alternating groups

“…Similar results for symmetric and alternating groups in arbitrary characteristic or Schur's double covers in characteristic 0 were obtained in [4,5,6,3,13] …”

“…Next, i and t 1 centralize n−3 , so the (conjugation) action of iu on n−3 is exactly the same as that of t 4 . It follows that B := n−3 · iu ∼ =Ŝn−3.…”

“…Now, using the known character values ofŜ 6 [12], we find that tr V (xt 1 t 2 ) equals 18, 3, 3, 12, and 12 for irreducible non-basic spin representations V ofŜ n of dimensions 4,8,8,10, and 10, respectively.…”

On mixed products of complex characters of the double covers of the symmetric groups

“…Information on special products and on the coefficients of special constituents have been obtained but there is no efficient combinatorial algorithm in sight for computing these products. In [1], products of S n -characters with few homogeneous components and homogeneous products of characters of the alternating group A n have been classified. In particular, there are no non-trivial homogeneous Kronecker products for S n , but there are such products for A n , when n is a square number (these are even irreducible).…”

On Kronecker products of spin characters of the double covers of the symmetric groups

“…In particular, the rectangular hull for the constituents in such products was found, and this was used for the classification of products with few homogeneous components; see [1] for this classification result and references to related work.…”