Baxterization for the dynamical Yang-Baxter equation

TL;DR

This paper develops a Baxterization method for the dynamical Yang-Baxter equation, introducing new operators and applying them to construct dynamical R matrices and integrable systems.

Contribution

It introduces local dynamical operators and a Baxterization process to generate dynamical R matrices, advancing the understanding of integrable models.

Findings

Reformulation of trigonometric degeneration of elliptic quantum groups

Construction of dynamical R matrices for ADE lattice models

Development of dynamical integrable spin chain systems

Abstract

The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of these operators, we get dynamical R matrix under some conditions. As applications, we reformulate trigonometric degeneration of elliptic quantum group representations and also get dynamical R matrix for critical ADE integrable lattice models. Through Baxterization, we construct some one dimensional integrable systems that are dynamical version of the Heisenberg spin chain.