Universal Vertex-IRF Transformation for Quantum Affine Algebras

Details Universal Vertex-IRF Transformation for Quantum Affine Algebras Universal Vertex-IRF Transformation for Quantum Affine Algebras

2007-07-06

arxiv.org/abs/0707.0955v1

Physics

Mathematical Physics

58 pages

Scientific paper

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.

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