Boltzmann Weights and Fusion Procedure for the Rational Seven-Vertex SOS Model.

We consider seven-vertex two-dimensional integrable statistical model. With the help of intertwining vector method we construct its counterpart integrable model of SOS type. More general models of both types are constructed by means of fusion procedure. For SOS models we calculate the Boltzmann weights in terms of terminating hypergeometric series 9F8. Then using the similarity transformation for R-operators we construct a new family of vertex models containing the 11-vertex model as a simplest representative. For this new set of models the vertex-SOS correspondence is constructed: we find the intertwining vectors and show that they do not depend on spectral parameter and the SOS statistical weights are similar to those obtained from the 7-vertex model. [ABSTRACT FROM AUTHOR]