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 = Ar 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