Fermionic Formulas for (<em>k</em>, 3)-admissible Configurations
Evgeny Mukhin
Indiana University Purdue University Indianapolis, United StatesBoris Feigin
Independent University of Moscow, Russian FederationM. Jimbo
University of Tokyo, JapanTetsuji Miwa
Kyoto University, JapanYoshihiro Takeyama
Graduate School of Pure and Applied Sciences, Ibaraki, Japan

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).
Cite this article
Evgeny Mukhin, Boris Feigin, M. Jimbo, Tetsuji Miwa, Yoshihiro Takeyama, Fermionic Formulas for (<em>k</em>, 3)-admissible Configurations. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 125–162
DOI 10.2977/PRIMS/1145475968