Some remarks on the eigenvalue problem for [formula omitted]n symmetric vertex and face models

Abstract

The eigenvalue solution of the transfer matrix of Belavin's Z n symmetric vertex model is further extended to the case of the model with the crossing parameter ω = 1 / L, here L is a nonzero positive integer. Then the so-called cyclic IRF model is defined and the eigenvalue solution of its transfer matrices is found. The eigenvalue spectrum of the IRF model at critical limit is shown to be the same as that of a modified many component six-vertex model, therefore the spectrums of both models are analysed with the quantum group SU q ( n).