2002/12/27 by B. Feigin, Boris Feigin, M. Jimbo +9
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.QA
paper · pdf · doi:10.48550/arxiv.math/0212347
30 pages
arxiv created 2002/12/27 · arxiv updated 2009/11/30
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 slr. 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).