Characters of Feigin-Stoyanovsky’s type subspaces of level one modules for affine Lie algebras of types A_l^(1) and D_4^(1)

We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types A_l^(1) and D_4^(1) to obtain character formulas. These descriptions naturally lead to systems of recurrence relations for which we also find solutions.