### Abstract

We give a complete description of the graded multiplicity space which appears in the Feigin-Loktev fusion product of graded Kirillov-Reshetikhin modules for all simple Lie algebras. This construction is used to obtain an upper bound formula for the fusion coefficients in these cases. The formula generalizes the case of g = A_{r} of our previous paper, where the multiplicities are generalized Kostka polynomials. In the case of other Lie algebras, the formula is the fermionic side of the X = M conjecture. In the cases where the Kirillov-Reshetikhin conjecture, regarding the decomposition formula for tensor products of KR-modules, has been proven in its original, restricted form, our result provides a proof of the conjectures of Feigin and Loktev regarding the fusion product multiplicities.

Original language | English (US) |
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Pages (from-to) | 270-294 |

Number of pages | 25 |

Journal | Journal of Algebra |

Volume | 308 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2007 |

### Keywords

- Kac-Moody algebras
- Representation theory

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Algebra*,

*308*(1), 270-294. https://doi.org/10.1016/j.jalgebra.2006.08.024