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

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.