Multivariable Vertex Models, the Temperley-Lieb Algebra and Link Polynomials

Abstract

We present a family of multivariable solvable vertex models associated with representations of the Temperley-Lieb algebra. We discuss free energy and correlation lengths for the multivariable models and also for the fusion models. We also discuss connection of the multivariable vertex models to Jones polynomials and link polynomials given by Akutsu-Wadati, which are associated with representations of U_q(sl(2, C)).