Recurrence relations for characters of affine Lie algebra $A_{\mathrm{\ell }}^{(1)}$

By using the known description of combinatorial bases for Feigin-Stoyanovsky’s type subspaces of standard modules for affine Lie algebra $\mathfrak{s}\mathfrak{l}(l+1,\mathbb{C}{)}^{\stackrel{~}{}}$, as well as certain intertwining operators between standard modules, we obtain exact sequences of Feigin-Stoyanovsky’s type subspaces at fixed level $k$. This directly leads to systems of recurrence relations for formal characters of those subspaces.