  By using the known description of combinatorial bases for
Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebra
$\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$, 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.
