The Lawrence-Krammer representation is a quantization of the symmetric square of the Burau representation
arXiv:1609.06663 · doi:10.1016/j.laa.2025.08.009
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
The following "Theorem 3.1. The polynomial K_Cl(X)(t, q) defined by (3.8) is the knot invariant." in the version 1 is wrong. Some additional corrections are made. 29.11.23 we corrected some formulas, see Remark 2.8, also MSC are corrected