Fermionic formulas for (κ, 3)-admissible configurations

Boris Feigin; Michio Jimbo; Tetsuji Miwa; Eugene Mukhin; Yoshihiro Takeyama

doi:10.2977/prims/1145475968

Fermionic formulas for (κ, 3)-admissible configurations

Boris Feigin^*
, Michio Jimbo
, Tetsuji Miwa
, Eugene Mukhin
, Yoshihiro Takeyama

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We obtain the fermionic formulas for the characters of (κ, 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-κ 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).

Original language	English
Pages (from-to)	125-162
Number of pages	38
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	40
Issue number	1
DOIs	https://doi.org/10.2977/prims/1145475968
State	Published - Mar 2004
Externally published	Yes

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Fermionic formulas for (κ, 3)-admissible configurations

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