Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

TL;DR

This paper uses the representation theory of Drinfeld doubles of dihedral groups to find solutions to the Yang-Baxter equation, extending the six-vertex model to higher dimensions with connections to the Fateev-Zamolodchikov model.

Contribution

It introduces a method to generate higher-dimensional solutions of the Yang-Baxter equation from the six-vertex model using tensor product graph techniques.

Findings

Recovered the six-vertex model solution from 2D representations.

Constructed higher-dimensional solutions as descendants of the six-vertex model.

Discussed links between these solutions and the Fateev-Zamolodchikov model.

Abstract

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.