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;
Academic Unit:	Faculty of Science and Engineering > Mathematics and 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:	http://www.degruyter.de/journals/jgt/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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