Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard $\tilde{\gsl}(\ell+1,\C)$-modules

Abstract

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of the type $A_\ell^{(1)}$. We find a combinatorial basis of Feigin-Stoyanovsky's type subspace $W(\Lambda)$ 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 $L(\Lambda)$ is obtained as an "inductive limit" of the basis of $W(\Lambda)$.