Integrability of the Six-Vertex model and the Yang-Baxter Groupoid

2022/10/26 by Naprienko, Slava
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2210.14883

Abstract

We study the Yang-Baxter equation for the R-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 R-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.

Related

• The Six-Vertex Yang-Baxter Groupoid
• Quantum superalgebras and the free-fermionic Yang-Baxter equation
• Schur Polynomials and the Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices
• Fifteen-vertex models with non-symmetric R matrices