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

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