Universal Vertex-IRF Transformation for Quantum Affine Algebras

TL;DR

This paper introduces a universal Vertex-IRF transformation for quantum affine algebras, extending previous work and connecting Vertex and Face solutions of the quantum dynamical Yang-Baxter equation.

Contribution

It constructs a universal Vertex-IRF transformation satisfying the generalized coBoundary equation for quantum affine algebras, with a simple Gauss decomposition using Sevostyanov's characters.

Findings

Universal solution extends previous work to quantum affine $U_q(A^{(1)}_r)$

Evaluation yields Baxter's transformation between 8-Vertex and IRF models

Solution has a simple Gauss decomposition

Abstract

We construct a universal Vertex-IRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical Yang-Baxter equation. This universal Vertex-IRF transformation satisfies the generalized coBoundary equation and is an extension of our previous work to the quantum affine $U_q(A^{(1)}_r)$ case. This solution has a simple Gauss decomposition which is constructed using Sevostyanov's characters of twisted quantum Borel algebras. We show that the evaluation of this universal solution in the evaluation representation of $U_q(A_1^{(1)})$ gives the standard Baxter's transformation between the 8-Vertex model and the IRF height model.