Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas

Eddy Ardonne, Rinat Kedem

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)270-294
Number of pages25
JournalJournal of Algebra
Volume308
Issue number1
DOIs
StatePublished - Feb 1 2007

Fingerprint

Multiplicity
Fusion
Module
Simple Lie Algebra
Generalized Polynomials
Tensor Product
Lie Algebra
Upper bound
Decompose
Generalise
Coefficient

Keywords

  • Kac-Moody algebras
  • Representation theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas. / Ardonne, Eddy; Kedem, Rinat.

In: Journal of Algebra, Vol. 308, No. 1, 01.02.2007, p. 270-294.

Research output: Contribution to journalArticle

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