Unitary Braid Representations with Finite Image

TL;DR

This paper characterizes specific unitary braid group representations with finite images, focusing on those with degrees linear or exponential in the number of strands, providing insights into their structure and limitations.

Contribution

It offers a classification of unitary braid representations with finite images based on their degree growth relative to the number of strands.

Findings

Characterization of linear degree representations

Classification of exponential degree finite image representations

Insights into the structure of finite image braid representations

Abstract

We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.