A modular branching rule for the generalized symmetric groups

We give a modular branching rule for certain wreath products as a generalization of Kleshchevʹs modular branching rule for the symmetric groups. Our result contains a modular branching rule for the complex reflection groups G(m,1,n), which are often called the generalized symmetric groups, in splitting fields for . Especially for m=2, which is the case of the Weyl groups of type B, we can give a modular branching rule in any field.