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

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

2005-04-18

arxiv.org/abs/math/0504364v2

Comm. Math. Phys. 264, 427-464, (2006).

Mathematics

Representation Theory

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

Scientific paper

10.1007/s00220-005-1486-3

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.

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