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Article Dans Une Revue Journal of Mathematical Physics Année : 2012

Universal vertex-IRF transformation for quantum affine algebras

Eric Buffenoir
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Philippe Roche
V. Terras

Résumé

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 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 Uq(A1(1)), it gives Baxter's well-known transformation between the 8-vertex model and the interaction-round-faces (IRF) height model.

Dates et versions

hal-00809429 , version 1 (09-04-2013)

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Citer

Eric Buffenoir, Philippe Roche, V. Terras. Universal vertex-IRF transformation for quantum affine algebras. Journal of Mathematical Physics, 2012, 53 (10), pp.103515. ⟨10.1063/1.4754699⟩. ⟨hal-00809429⟩
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