On the parametrization of solutions of the Yang--Baxter equations

Abstract

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.

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References in corpus (2)

• The complete solution to the constant quantum Yang-Baxter equation in two dimensions
• Singularity, complexity, and quasi--integrability of rational mappings