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

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

2002-10-11

arxiv.org/abs/math/0210168v3

Mathematics

Quantum Algebra

44 pages, no figures, Typos are corrected. Accepted for the publication in Comm. Math. Phys

Scientific paper

10.1007/s00220-003-0893-6

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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