Yang-Baxter Relations in Terms of n−j Symbols of su_q(2) Algebra

Abstract

A trigonometric function parametrization of Yang-Baxter (Y-B) relations is described in terms of n−j symbols of su_q(2), a deformation of su(2). The formalism starts with deduction of the Y-B relation for the IRF (interaction round a face) model of su_q(2) from a general operator relation for the vertex model. The relation obtained for the IRF model is transformed into the Y-B relation for the vertex model using the property that the 3−j symbol is an asymptotic limit of the 6−j symbol. A class of very general solutions to Y-B equations is also presented. This solution of the IRF model with infinite rapidity parameters is linked to a symmetry of the 12−j symbol of the second kind.