Character formulas for Feigin-Stoyanovsky's type subspaces of standard $\mathfrak{sl}(3, \mathbb{C})^{\widetilde{}}$-modules

Abstract

Exact sequences of Feigin-Stoyanovsky's type subspaces for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$ lead to systems of recurrence relations for formal characters of those subspaces. By solving the corresponding system for $\mathfrak{sl}(3,\mathbb{C})^{\widetilde{}}$, we obtain a new family of character formulas for all Feigin-Stoyanovsky's type subspaces at general level.