Colored version for Lawrence representations

TL;DR

This paper establishes an explicit link between the Gassner representation and quantum sl(2), and constructs colored versions of BKL and Lawrence's representations with explicit matrices.

Contribution

It introduces a new explicit isomorphism and constructs colored versions of key braid group representations with detailed matrix forms.

Findings

Explicit isomorphism between Gassner and quantum sl(2) representations

Construction of colored BKL and Lawrence's representations

Provision of explicit matrices for these representations

Abstract

We give an explicit isomorphism between the Gassner representation and the first weight level of a representation of quantum sl(2). Then we construct and provide matrices for colored versions of the BKL representation and higher Lawrence's representations.