Universal Vertex-IRF Transformation for Quantum Affine Algebras

2007/07/06 by Buffenoir, Eric, Roche, Philippe, Terras, Véronique
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0707.0955

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(A₁⁽¹⁾) gives the standard Baxter's transformation between the 8-Vertex model and the IRF height model.

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