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

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.

arXiv comment44 pages, no figures, Typos are corrected. Accepted for the publication in Comm. Math. Phys

References in corpus (6)

• Null-vectors in Integrable Field Theory
• Counting the local fields in SG theory.
• The space of local operators in perturbed conformal field theories,
• The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory
• On solutions of the KZ and qKZ equations at level zero
• Completeness of the Hypergeometric Solutions of the qKZ Equation at Level Zero

Cited by in corpus (1)

• Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles