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Licensed Unlicensed Requires Authentication Published by De Gruyter February 8, 2010

Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules

  • Harald Ellers and John Murray
From the journal Journal of Group Theory

Abstract

Let Σn be the symmetric group of degree n, and let F be a field of characteristic p. Suppose that λ is a partition of n + 1, that α and β are partitions of n that can be obtained by removing a node of the same residue from λ, and that α dominates β. Let Sα and Sβ be the Specht modules, defined over F, corresponding to α, respectively β. We use Jucys–Murphy elements to give a very simple description of a non-zero homomorphism SαSβ. Following Lyle, we also give an explicit expression for the homomorphism in terms of semi-standard homomorphisms. Our methods furnish a lower bound for the Jantzen submodule of Sβ that contains the image of the homomorphism. Our results allow us to describe completely the structure of the ring EndFΣn(SλΣn) when p ≠ 2.

Received: 2009-01-30
Revised: 2009-07-31
Published Online: 2010-02-08
Published in Print: 2010-July

© de Gruyter 2010

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