Universal spectral parameter-dependent Lax operators for the Drinfeld double of the dihedral group $D_3$

TL;DR

This paper introduces universal spectral parameter-dependent Lax operators based on the Drinfeld double of the dihedral group D_3, leading to matrix solutions of the Yang-Baxter equation with spectral parameter.

Contribution

It presents new universal Lax operators for D(D_3) that generate solutions to the Yang-Baxter equation, expanding the algebraic tools for integrable models.

Findings

Two universal spectral parameter-dependent Lax operators are constructed.

Representation of D(D_3) yields matrix solutions to the Yang-Baxter equation.

Provides a framework for integrable models related to the dihedral group D_3.

Abstract

Two universal spectral parameter-dependent Lax operators are presented in terms of the elements of the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. Applying representations of $D(D_3)$ to these yields matrix solutions of the Yang-Baxter equation with spectral parameter.