Abstract
This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable -modules. We give formulas for the q-characters of any highest-weight integrable module of 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 . We also give the fermionic formulas for the q-characters of the (non-level-restricted) fusion products of rectangular highest-weight integrable -modules.
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Ardonne, E., Kedem, R. & Stone, M. Fermionic Characters and Arbitrary Highest-Weight Integrable -Modules. Commun. Math. Phys. 264, 427–464 (2006). https://doi.org/10.1007/s00220-005-1486-3
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DOI: https://doi.org/10.1007/s00220-005-1486-3