Endomorphism algebras of 2-row permutation modules over characteristic 3

Abstract

Given $r\in \mathbf{N},$ let $\lambda$ be a partition of $r$ with at most two parts. Let $\mathbf{F}$ be a field of characteristic 3. Write $M^{\lambda }$ for the $\mathbf{F}{S}_r$-permutation module corresponding to the action of the symmetric group $S_r$ on the cosets of the maximal Young subgroup $S_{\lambda }.$ We construct a full set of central primitive idempotents in ${\text{End}}_{\mathbf{F}{S}_r}(M^{\lambda })$ in this case. We also determine the Young module corresponding to each primitive idempotent that we construct.

23 pages. Updated with comments from referee incorporated