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

  • Evgeny Mukhin

    Indiana University Purdue University Indianapolis, United States
  • Boris Feigin

    Independent University of Moscow, Russian Federation
  • M. Jimbo

    University of Tokyo, Japan
  • Tetsuji Miwa

    Kyoto University, Japan
  • Yoshihiro Takeyama

    Graduate School of Pure and Applied Sciences, Ibaraki, Japan


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