Universal Vertex-IRF Transformation for Quantum Affine Algebras

E. Buffenoir (1) , P. Roche (1) , V. Terras (1)

1 LPTA - Laboratoire de Physique Théorique et Astroparticules

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.

Mots clés: Vertex-IRF Transformation; Quantum Affine Algebra; Dynamical Quantum Groups; 8 vertex model

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Algèbres quantiques [math.QA]

E. Buffenoir, P. Roche, V. Terras. Universal Vertex-IRF Transformation for Quantum Affine Algebras. 2007. ⟨hal-00160579⟩