Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules
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Harald Ellers
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
Articles in the same Issue
- A note on the Green theory in the Clifford-theoretic context of a defect zero p-block of a normal subgroup of a finite group
- A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups
- Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules
- Some linear actions of finite groups with q′-orbits
- Semi-rational solvable groups
- Finite non-abelian 2-groups such that any two distinct minimal non-abelian subgroups have cyclic intersection
- A note on the p-supersolvability of finite groups
- Vertex-transitive tournaments of order a product of two distinct primes
- On the derived length of the unit group of a group algebra
- On the subgroups with non-trivial Möbius number
- Subgroups of free groups and primitive elements
- Small index subgroups of the mapping class group
Articles in the same Issue
- A note on the Green theory in the Clifford-theoretic context of a defect zero p-block of a normal subgroup of a finite group
- A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups
- Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules
- Some linear actions of finite groups with q′-orbits
- Semi-rational solvable groups
- Finite non-abelian 2-groups such that any two distinct minimal non-abelian subgroups have cyclic intersection
- A note on the p-supersolvability of finite groups
- Vertex-transitive tournaments of order a product of two distinct primes
- On the derived length of the unit group of a group algebra
- On the subgroups with non-trivial Möbius number
- Subgroups of free groups and primitive elements
- Small index subgroups of the mapping class group
