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A modular branching rule for the generalized symmetric groups

Shunsuke Tsuchioka
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Abstract

We give a modular branching rule for certain wreath products as a generalization of Kleshchev's 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 $\mathbb{Z}/m\mathbb{Z}$. 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. Our proof is elementary in that it is essentially a combination of Frobenius reciprocity, Mackey theorem, Clifford's theory and Kleshchev's modular branching rule.

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Shunsuke Tsuchioka. 2006-10-03. A modular branching rule for the generalized symmetric groups. https://arxiv.org/abs/math/0610101

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