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

Kailash C. Misra, Evan A. Wilson

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 seemi…