engleski

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

Let g^~ be an affine Lie algebra of the type A_l^(1). Suppose we're given a Z-gradation of the corresponding simple finite-dimensional Lie algebra g=g_-1+g_0+g_1 ; then we also have the induced Z-gradation of the affine Lie algebra g^~=g^~_-1+g^~_0+g^~_1. Let L(Lambda) be a standard module of level 1. Feigin-Stoyanovsky's type subspace W(Lambda) is the g^~_1-submodule of L(Lambda) generated by the highest-weight vector v_Lambda, W(Lambda)=U(g^~_1) v_Lambda \subset L(Lambda). We find a combinatorial basis of W(Lambda) given in terms of difference and initial conditions.

Affine Lie algebras; Combinatorial bases

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