Resonance relations for solutions of the elliptic QKZB equations, fusion rules, and eigenvectors of transfer matrices of restricted interaction-round-a-face models

Conformal blocks for the WZW model on tori can be represented by vector val ued Weyl anti-symmetric theta functions on the Cartan subalgebra satisfying vanishing conditions on root hyperplanes. We introduce a quantum version o f these vanishing conditions in the sit 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 ro w-to-row transfer matrices. In the language of IRF models the vanishing con ditions turn out to be equivalent to the sit fusion rules defining restrict ed models.