Baxterization, dynamical systems, and the symmetries of integrability

TL;DR

This paper uses the automorphism group of Yang-Baxter equations to solve the baxterization problem, revealing new symmetries, parametrizations, and dynamical systems beyond traditional integrability contexts.

Contribution

It introduces a novel approach to baxterization via Coxeter group symmetries, extending the understanding of integrability and non-integrable models.

Findings

Elliptic parametrization of the sixteen-vertex model

Identification of a non-linear Coxeter group acting on matrices

Development of discrete dynamical systems related to integrability

Abstract

We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group acting on matrices, and exists as such, {\em 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 complexity of iterations.