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

Ellers, Harald and Murray, John (2010) Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules. Journal of Group Theory, 13 (4). pp. 477-501. ISSN 1433-5883

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Abstract

Let n be the symmetric group of degree n, and let F be a field of characteristic p 6= 2. Suppose that  is a partition of n+1, that and are partitions of n that can be obtained by removing a node of the same residue from , and that dominates . Let S and S be the Specht modules, defined over F, corresponding to , respectively . We give a very simple description of a non-zero homomorphism  : S → S and present a combinatorial proof of the fact that dimHomFn(S , S ) = 1. As an application, we describe completely the structure of the ring EndFn(S ↓n ). Our methods furnish a lower bound for the Jantzen submodule of S that contains the image of .

Item Type: Article
Keywords: Carter–Payne homomorphisms; branching rules; endomorphism rings; Specht modules;
Subjects: Science & Engineering > Mathematics & Statistics
Item ID: 2058
Depositing User: Dr. John Murray
Date Deposited: 20 Jul 2010 15:57
Journal or Publication Title: Journal of Group Theory
Publisher: de Gruyter
Refereed: No
URI:

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