Specht module branching rules for wreath products of symmetric groups
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 609-628.

We review a class of modules for the wreath product S m 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 S n and S m 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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DOI: 10.5802/alco.223
Classification: 05E10
Keywords: branching rules, Specht modules, symmetric groups
Green, Reuben 1

1 Pembroke College St Aldate’s Oxford OX1 1DW
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Green, Reuben. Specht module branching rules for wreath products of symmetric groups. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 609-628. doi : 10.5802/alco.223. https://alco.centre-mersenne.org/articles/10.5802/alco.223/

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