Universal vertex-IRF transformation for quantum affine algebras

Abstract

We construct a universal solution of the generalized coboundary equation in the case of quantum affine algebras, which is an extension of our previous work to $U_q(A^{(1)}_r)$Uq(Ar(1)). This universal solution has a simple Gauss decomposition which is constructed using Sevostyanov's characters of twisted quantum Borel algebras. We show that in the evaluation representations it gives a vertex-face transformation between a vertex type solution and a face type solution of the quantum dynamical Yang-Baxter equation. In particular, in the evaluation representation of $U_q(A_1^{(1)})$Uq(A1(1)), it gives Baxter's well-known transformation between the 8-vertex model and the interaction-round-faces (IRF) height model.