J. Hietarinta ; C. Viallet - On the parametrization of solutions of the Yang--Baxter equations

ocnmp:10204 - Open Communications in Nonlinear Mathematical Physics, December 1, 2022, Volume 2 - https://doi.org/10.46298/ocnmp.10204
On the parametrization of solutions of the Yang--Baxter equationsArticle

Authors: J. Hietarinta ; C. Viallet

    We study all five-, six-, and one eight-vertex type two-state solutions of the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13} A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of these solution. Starting with algebraic solutions, whose parameters have no specific interpretation, and then using these symmetries we can construct a parametrization where we can identify global, color and spectral parameters. We show in particular how the distribution of these parameters may be changed by a change of gauge.


    Volume: Volume 2
    Published on: December 1, 2022
    Accepted on: November 6, 2022
    Submitted on: October 25, 2022
    Keywords: Mathematics - Quantum Algebra,High Energy Physics - Theory

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