### 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 1 2006 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Fermionic characters and arbitrary highest-weight integrable sl̂ _{r+1}-modules.** / Ardonne, Eddy; Kedem, Rinat; Stone, Michael.

Research output: Contribution to journal › Article

_{r+1}-modules',

*Communications in Mathematical Physics*, vol. 264, no. 2, pp. 427-464. https://doi.org/10.1007/s00220-005-1486-3

}

TY - JOUR

T1 - Fermionic characters and arbitrary highest-weight integrable sl̂r+1-modules

AU - Ardonne, Eddy

AU - Kedem, Rinat

AU - Stone, Michael

PY - 2006/6/1

Y1 - 2006/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33645974574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645974574&partnerID=8YFLogxK

U2 - 10.1007/s00220-005-1486-3

DO - 10.1007/s00220-005-1486-3

M3 - Article

AN - SCOPUS:33645974574

VL - 264

SP - 427

EP - 464

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -