Abstract
Let Σn be the symmetric group of degree n, and let F be a field of characteristic p. Suppose that λ is a partition of n + 1, that α and β are partitions of n that can be obtained by removing a node of the same residue from λ, and that α dominates β. Let Sα and Sβ be the Specht modules, defined over F, corresponding to α, respectively β. We use Jucys–Murphy elements to give a very simple description of a non-zero homomorphism Sα → Sβ. Following Lyle, we also give an explicit expression for the homomorphism in terms of semi-standard homomorphisms. Our methods furnish a lower bound for the Jantzen submodule of Sβ that contains the image of the homomorphism. Our results allow us to describe completely the structure of the ring EndFΣn(Sλ ↓Σn) when p ≠ 2.
© de Gruyter 2010