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

J. Hietarinta·C. Viallet
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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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J. Hietarinta, C. Viallet. 1995-04-28. On the parametrization of solutions of the Yang--Baxter equations. https://doi.org/10.46298/ocnmp.10204

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