Yang-Baxter solutions from commuting operators

TL;DR

This paper introduces new solutions to the Yang-Baxter equation using commuting operators, expanding the class of integrable models with multidimensional spectral parameters and analyzing their algebraic structures.

Contribution

It constructs novel R-matrices depending on commuting operators, including additive and non-additive parameters, and explores their algebraic and spectral properties.

Findings

Constructed R-matrices with multidimensional spectral parameters

Demonstrated solutions satisfy the colored Yang-Baxter equation

Analyzed the associated Yang-Baxter algebra and transfer matrix spectrum

Abstract

We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They change with the representation of the latter. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.