Qubit representations of the braid groups from generalized Yang-Baxter matrices

TL;DR

This paper investigates how certain generalized Yang-Baxter matrices derived from anyons in metaplectic modular categories produce specific qubit representations of braid groups, elucidating their algebraic structure.

Contribution

It precisely identifies the images of qubit braid group representations arising from generalized Yang-Baxter matrices in metaplectic categories.

Findings

Explicit description of the images of these braid group representations.

Connection between generalized Yang-Baxter matrices and metaplectic anyons.

Enhanced understanding of the algebraic structure of these representations.

Abstract

Generalized Yang-Baxter matrices sometimes give rise to braid group representations. We identify the exact images of some qubit representations of the braid groups from generalized Yang-Baxter matrices obtained from anyons in the metaplectic modular categories.