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Residues of q-Hypergeometric Integrals and Characters of Affine Lie Algebras

Atsushi Nakayashiki
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Abstract

We study certain subspaces of solutions to the sl_2 rational qKZ equation at level zero. Each subspace is specified by the vanishing of the residue at a certain divisor which stems from models in two dimensional integrable field theories. We determine the character of the subspace which is parametrized by the number of variables and the sl_2 weight of the solutions. The sum of all characters with a fixed weight gives rise to the branching functions of the irreducible representations of sl_2 in the level one integrable highest weight representations of \hat{sl_2}. It is written in the fermionic form.

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BibTeXRIS

Atsushi Nakayashiki. 2003-08-19. Residues of q-Hypergeometric Integrals and Characters of Affine Lie Algebras. https://doi.org/10.1007/s00220-003-0893-6

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