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Baxterization, dynamical systems, and the symmetries of integrability

  • C. -M. Viallet
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 436)

Abstract

We resolve the ‘baxterization’ problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, ...) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group acting on matrices, and exists as such, beyond the narrow context of strict integrability. It yields among other things an unexpected elliptic parametrization of the non-integrable sixteen-vertex model. It provides us with a class of discrete dynamical systems, and we address some related problems, such as characterizing the growth of the complexity of iterations.

Keywords

Projective Space Coxeter Group Discrete Dynamical System Vertex Model Infinite Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • C. -M. Viallet
    • 1
  1. 1.Laboratoire de Physique Théorique et des Hautes Energies, Centre National de la Recherche ScientifiqueUniversité de Paris 6- Paris 7Parisz Cedex 05France

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