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

Eddy Ardonne, Rinat Kedem, Michael Stone

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)427-464
Number of pages38
JournalCommunications in Mathematical Physics
Volume264
Issue number2
DOIs
StatePublished - Jun 1 2006

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modules
Module
Arbitrary
Fusion
products
Irreducible Module
fusion
Inverse matrix
Generalized Polynomials
Tensor Product
Linear Combination
Multiplicity
entry
polynomials
Character
tensors
Coefficient
coefficients
matrices

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Fermionic characters and arbitrary highest-weight integrable sl̂r+1-modules. / Ardonne, Eddy; Kedem, Rinat; Stone, Michael.

In: Communications in Mathematical Physics, Vol. 264, No. 2, 01.06.2006, p. 427-464.

Research output: Contribution to journalArticle

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