Theta function solutions of the quantum Knizhnik–Zamolodchikov–Bernard equation for a face model

Abstract

International audienceWe consider the quantum Knizhnik–Zamolodchikov–Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model, these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions