Fermionic characters of arbitrary highest-weight integrable sl_{r+1}-modules

Abstract

We give a formula for the q-characters of arbitrary highest-weight integrable modules of sl_{r+1} as a linear combination of the fermionic q-characters of special fusion products of integrable modules. The coefficients in the sum are entries of the inverse matrix of generalized Kostka polynomials, which are in Z[q^{-1}]. In this paper we prove the relation between the character of the Feigin-Loktev graded tensor product and the generalized Kostka polynomial. We also prove the fermionic formula for the q-characters of the (unrestricted) fusion products of rectangular highest-weight integrable g-modules.

31 pages, 2 figures; v2: final version, to appear in CMP

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Cited by in corpus (4)

• Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas
• The intermediate vertex subalgebras of the lattice vertex operator algebras
• Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$