Fermionic characters and arbitrary highest-weight integrable sl̂r+1-modules

Eddy Ardonne, Rinat Kedem, Michael Stone

Research output: Contribution to journalArticle


This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable sl̂r+1-modules. We give formulas for the q-characters of any highest-weight integrable module of sl̂r+1 as a linear combination of the fermionic q-characters of the fusion products of a special set of integrable modules. The coefficients in the sum are the entries of the inverse matrix of generalized Kostka polynomials in q -1. We prove the conjecture of Feigin and Loktev regarding the q-multiplicities of irreducible modules in the graded tensor product of rectangular highest weight-modules in the case of sl̂r+1. We also give the fermionic formulas for the q-characters of the (non-level-restricted) fusion products of rectangular highest-weight integrable sl̂r+1.

Original languageEnglish (US)
Pages (from-to)427-464
Number of pages38
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Jun 1 2006


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this