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. 477501.
ISSN 14335883
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 nonzero 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: 

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