On Tensor Product Decomposition of $\hat{\mathfrak{sl}}(n)$ Modules (1109.2478v1)

Abstract: We decompose the $\hat{\mathfrak{sl}}(n)$-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 $n=2,3$.