dorsal/arxiv
View SchemaOn the parametrization of solutions of the Yang--Baxter equations
| Authors | J. Hietarinta, C. Viallet |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9504028 |
| URL | https://arxiv.org/abs/q-alg/9504028 |
| DOI | 10.46298/ocnmp.10204 |
| Journal | Open Communications in Nonlinear Mathematical Physics, Volume 2 (December 1, 2022) ocnmp:10204 |
| License | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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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"abstract": "We study all five-, six-, and one eight-vertex type two-state solutions of\nthe Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13}\nA_{12}$, and analyze the interplay of the `gauge\u0027 and `inversion\u0027 symmetries of\nthese solution. Starting with algebraic solutions, whose parameters have no\nspecific interpretation, and then using these symmetries we can construct a\nparametrization where we can identify global, color and spectral parameters. We\nshow in particular how the distribution of these parameters may be changed by a\nchange of gauge.",
"arxiv_id": "q-alg/9504028",
"authors": [
"J. Hietarinta",
"C. Viallet"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.46298/ocnmp.10204",
"journal_ref": "Open Communications in Nonlinear Mathematical Physics, Volume 2\n (December 1, 2022) ocnmp:10204",
"license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
"title": "On the parametrization of solutions of the Yang--Baxter equations",
"url": "https://arxiv.org/abs/q-alg/9504028"
},
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