The Lawrence-Krammer representation is a quantization of the symmetric square of the Burau representation

TL;DR

This paper demonstrates that the Lawrence-Krammer representation arises from quantizing the symmetric square of the Burau representation, providing a new perspective and tools for constructing braid group representations.

Contribution

It establishes a novel link between the Lawrence-Krammer and Burau representations through quantization, enabling new approaches to braid group representations.

Findings

Lawrence-Krammer is a quantization of the symmetric square of Burau

New representations of braid groups can be constructed using this connection

Provides a deeper understanding of the relationship between key braid group representations

Abstract

We show that the Lawrence--Krammer representation can be obtained as the quantization of the symmetric square of the Burau representation. This connection allows us to construct new representations of braid groups