Endomorphism Rings of Some Young Modules

Abstract

Let $Σ_r$ be the symmetric group acting on $r$ letters, $K$ be a field of characteristic 2 and $λ$ and $μ$ be partitions of $r$ in at most two parts. Denote the permutation module corresponding to the Young subgroup $Σ_λ$ in $Σ_r$ by $M^λ$, and the indecomposable Young module by $Y^μ$. We give an explicit presentation of the endomorphism algebra ${\rm End}_{K[Σ_r]}(Y^μ)$, using the idempotents found by Doty, Erdmann and Henke in [1].