Multiplicities of some maximal dominant weights of the $\widehat{s\ell }(n)$-modules $V(k{\Lambda }_0)$

Rebecca L. Jayne, Kailash C. Misra

For $n\ge 2$ consider the affine Lie algebra $\widehat{s\ell }(n)$ with simple roots $\{{\alpha }_i\mid 0\le i\le n-1\}$. Let $V(k{\Lambda }_0),k\in {\mathbb{Z}}_{\ge 1}$ denote the integ…