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 $W(\Lambda )$.

27 pages, 7 figures