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
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 .
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