Some remarks about the faithfulness of the Burau representation of Artin--Tits groups

2024/08/30 by Bapat, Asilata, Queffelec, Hoel · 2 citations
#18G80 #18N25 #20F36 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2409.00144

Abstract

We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not faithful in affine type A₃, and not faithful over several finite rings in type D₄, using an algorithmic approach based on categorical methods that generalize Bigelow's curve strategy outside of type A.

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• A fast algorithm for the Hecke representation of the braid group, and applications to the computation of the HOMFLY-PT polynomial and the search for interesting braids
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