Discrete Real Specializations of Sesquilinear Representations of the Braid Groups

TL;DR

This paper introduces a method to find discrete real specializations of sesquilinear braid group representations using Salem numbers, with applications to Jones and BMW representations and insights into group commensurability.

Contribution

It presents a novel process leveraging Salem numbers to identify discrete real specializations of sesquilinear braid group representations, specifically applied to Jones and BMW cases.

Findings

Successful application to Jones and BMW representations

Identification of conditions for discreteness and real specialization

Insights into the commensurability of the resulting groups

Abstract

This paper gives a process for finding discrete real specializations of sesquilinear representations of the braid groups using Salem numbers. This method is applied to the Jones and BMW representations, and some details on the commensurability of the target groups are given.