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