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arXiv · 2001.06813

Specht module branching rules for wreath products of symmetric groups

Reuben Green
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Abstract

We review a class of modules for the wreath product S(m) wr 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) wr S(n) and S(m) wr 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.

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BibTeXRIS

Reuben Green. 2020-01-19. Specht module branching rules for wreath products of symmetric groups. https://arxiv.org/abs/2001.06813

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