On multiplicities of maximal weights of $\widehat{sl}(n)$-modules

Rebecca L. Jayne, Kailash C. Misra

We determine explicitly the maximal dominant weights for the integrable highest weight $\widehat{sl}(n)$-modules $V((k-1){\Lambda }_0+{\Lambda }_s)$, $0\le s\le n-1$, $k\ge 2$. We give a conjec…