The classification of Wada-type representations of braid groups

TL;DR

This paper classifies Wada-type representations of braid groups and solutions to a related Yang-Baxter equation, confirming that only seven types exist up to symmetries, advancing understanding of braid group representations.

Contribution

It provides a complete classification of Wada-type braid group representations and solutions to a specific Yang-Baxter equation variant, confirming Wada's conjecture.

Findings

Seven types of Wada-type representations identified

Classification up to symmetries established

Solutions to the adapted Yang-Baxter equation characterized

Abstract

We give a classification of Wada-type representations of the braid groups, and solutions of a variant of the set-theoretical Yang-Baxter equation adapted to the free-product group structure. As a consequence, we prove Wada's conjecture: There are only seven types of Wada-type representations up to certain symmetries.