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

2016/09/21 by Kosyak, Alexandre
#20F36 #20G42 #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1609.06663

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

Related

• Faithfulness of the Lawrence representation of braid groups
• Parameters for which the Lawrence-Krammer representation is reducible
• The pro-nilpotent Lawrence-Krammer-Bigelow representation
• The Lawrence--Krammer representation is unitary
• Representations of braid groups