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

Abstract

We decompose the $\widehat{\mathfrak{sl}}(n)$-module $V({\Lambda }_0)\otimes V({\Lambda }_i)$ and give generating function identities for the outer multiplicities. In the process we discover some seemingly new partition identities for $n=3,4$.

arXiv comment15 pages. arXiv admin note: substantial text overlap with arXiv:1109.2478