Endomorphism Rings of Some Young Modules

Abstract

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

arXiv comment11 pages

References in corpus (2)

• Young module multiplicities and classifying the indecomposable Young permutation modules
• Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2)