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 for specific groups, advancing the understanding of integrable models.

Contribution

It introduces a general functional definition of the quantum R-matrix and shows a method to obtain finite-dimensional solutions for particular groups.

Findings

Functional definition of quantum R-matrix provided

Finite-dimensional R-matrices derived for O(2) and translation groups

Advances in understanding solutions to the Yang-Baxter equation

Abstract

A general functional definition of the infinite dimensional quantum R-matrix satisfying the Yang-Baxter equation is given. A procedure for extracting a finite dimensional R-matrix from the general definition is demonstrated for the particular cases of the group O(2) and of the group of translations.