On Tensor Product Decomposition of $\widehat{\mathfrak{sl}}(n)$ Modules

Abstract

We decompose the $\widehat{\mathfrak{sl}}(n)$-module $V({\Lambda }_0)\otimes V({\Lambda }_0)$ and give generating function identities for the outer multiplicities. In the process we discover some seemingly new partition identities in the cases $n=2,3$.