Parametrization of representations of braid groups

TL;DR

This paper introduces a method to generate and analyze representations of braid groups, providing conditions for non-unitary cases and examples of irreducible representations across finite and infinite dimensions.

Contribution

It presents a novel approach for parametrizing braid group representations and establishes criteria for non-unitary representations, expanding the understanding of their structure.

Findings

Method to produce braid group representations

Conditions for non-unitary representations

Examples of irreducible finite and infinite-dimensional representations

Abstract

We give a method to produce representations of the braid group $B_n$ of $n-1$ generators ($n\leq \infty$). Moreover, we give sufficient conditions over a non unitary representation for being of this type. This method produces examples of irreducible representations of finite and infinite dimension.