Fermionic Formulas for (<em>k</em>, 3)-admissible Configurations

Abstract

We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r = 2 and r = 3. This combinatorial object appears as a label of a basis of certain subspace W(Λ) of level-k integrable highest weight module of sl^r. The dual space of W(Λ) is embedded into the space of symmetric polynomials. We introduce a filtration on this space and determine the components of the associated graded space explicitly by using vertex operators. This implies a fermionic formula for the character of W(Λ).