Specht module branching rules for wreath products of symmetric groups

Abstract

We review a class of modules for the wreath product S(m) wr S(n) of two symmetric groups which are analogous to the Specht modules of the symmetric group, and prove a pair of branching rules for this family of modules. These branching rules describe the behaviour of these wreath product Specht modules under restriction to the wreath products S(m-1) wr S(n) and S(m) wr S(n-1). In particular, we see that these restrictions of wreath product Specht modules have Specht module filtrations, and we obtain combinatorial interpretations of the multiplicities in these filtrations.