Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of higher-level standard sl^~(l+1, C)-modules

Let g^~ be an affine Lie algebra of the type A_l^(1). We find a combinatorial basis of Feigin–Stoyanovsky's type subspace W(Λ) given in terms of difference and initial conditions. Linear independence of the generating set is proved inductively by using coefficients of intertwining operators. A basis of the standard g^~-module L(Λ) is obtained as an “inductive limit” of the basis of W(Λ).