Integrability of the Six-Vertex model and the Yang-Baxter Groupoid
Quantum Algebra
2022-10-27 v1 Mathematical Physics
math.MP
Abstract
We study the Yang-Baxter equation for the -matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized solutions which generalize the -matrices from the affine quantum (super)-groups. Then we give a new parametrization of the Yang-Baxter equation by a groupoid of non-free-fermionic matrices. In the appendix, we study the general algebraic structure of the solutions of the Yang-Baxter and formulate a conjecture that extends the conjecture by Brubaker, Bump, and Friedberg that the composition law on the Yang-Baxter solutions is always associative.
Keywords
Cite
@article{arxiv.2210.14883,
title = {Integrability of the Six-Vertex model and the Yang-Baxter Groupoid},
author = {Slava Naprienko},
journal= {arXiv preprint arXiv:2210.14883},
year = {2022}
}