Some functional solutions of the Yang-Baxter equation

TL;DR

This paper provides a functional framework for the quantum R-matrix satisfying the Yang-Baxter equation and demonstrates how to derive finite-dimensional solutions from this general approach, focusing on the SU(2) case.

Contribution

It introduces a general functional definition of the quantum R-matrix and shows a method to extract finite-dimensional solutions, advancing the understanding of Yang-Baxter equation solutions.

Findings

Defined a functional form of the infinite-dimensional quantum R-matrix.

Presented a procedure to obtain finite-dimensional R-matrices from the general form.

Applied the method explicitly to the SU(2) group case.

Abstract

A general functional definition of the infinite dimensional quantum $R$-matrix satisfying the Yang-Baxter equation is given. A procedure for the extracting a finite dimensional $R$-matrix from the general definition is demonstrated in a particular case when the group $SU(2)$ takes place.