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We use combinatorial description of bases of Feigin-Stoyanovsky's typesubspaces of standard modules of level 1 for affine Lie algebras of types$A_\ell^{(1)}$ and $D_4^{(1)}$ to obtain character formulas. These descriptionsnaturally lead to systems of recurrence relations for which we also findsolutions.

Characters of Feigin-Stoyanovsky's type subspaces of level one modules for affine Lie algebras of types $A_\ell^{(1)}$ and $D_4^{(1)}$