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We review a class of modules for the wreath product S(m) wr S(n) of twosymmetric groups which are analogous to the Specht modules of the symmetricgroup, and prove a pair of branching rules for this family of modules. Thesebranching rules describe the behaviour of these wreath product Specht modulesunder restriction to the wreath products S(m-1) wr S(n) and S(m) wr S(n-1). Inparticular, we see that these restrictions of wreath product Specht moduleshave Specht module filtrations, and we obtain combinatorial interpretations ofthe multiplicities in these filtrations.

Specht module branching rules for wreath products of symmetric groups