### Abstract

This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable sl̂_{r+1}-modules. We give formulas for the q-characters of any highest-weight integrable module of sl̂_{r+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 sl̂_{r+1}. We also give the fermionic formulas for the q-characters of the (non-level-restricted) fusion products of rectangular highest-weight integrable sl̂_{r+1}.

Original language | English (US) |
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Pages (from-to) | 427-464 |

Number of pages | 38 |

Journal | Communications in Mathematical Physics |

Volume | 264 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2006 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics