RESONANCE RELATIONS FOR SOLUTIONS OF THE ELLIPTIC QKZB EQUATIONS, FUSION RULES, AND EIGENVECTORS OF TRANSFER MATRICES OF RESTRICTED INTERACTION-ROUND-A-FACE MODELS

Source abstract

Conformal blocks for the WZW model on tori can be represented by vector valued Weyl anti-symmetric theta functions on the Cartan subalgebra satisfying vanishing conditions on root hyperplanes. We introduce a quantum version of these vanishing conditions in the sl 2 case. They are compatible with the qKZB equations and are obeyed by the hypergeometric solutions as well as by their critical level counterpart, which are Bethe eigenfunctions of IRF row-to-row transfer matrices. In the language of IRF models the vanishing conditions turn out to be equivalent to the sl 2 fusion rules defining restricted models.