Specht module branching rules for wreath products of symmetric groups

We review a class of modules for the wreath product S m 2 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 2 S n and S m 2 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.