Some properties of Specht modules for the wreath product of symmetric groups

We investigate a class of modules for the wreath product Sm wr Sn of two symmetric groups which are analogous to the Specht modules of the symmetric group, and prove a range of properties for these modules which demonstrate this analogy. In particular, we prove analogues of the Specht module branching rule, we obtain results on homomorphisms and extensions between these modules, and, over an algebraically closed field whose characteristic is neither 2 nor 3, we prove that, if a module for Sm wr Sn has a filtration by these Specht module analogues, then the multiplicities with which they occur do not depend on the choice of a filtration.