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

摘要

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 $widehat{sl_2}$ . It is written in the fermionic form.