Lawrence-Krammer-Bigelow representations and dual Garside length of braids

Details Lawrence-Krammer-Bigelow representations and dual Garside length of braids Lawrence-Krammer-Bigelow representations and dual Garside length of braids

2012-01-04

arxiv.org/abs/1201.0957v1

Mathematics

Group Theory

Scientific paper

We show that the span of the variable $q$ in the Lawrence-Krammer-Bigelow representation matrix of a braid is equal to the twice of the dual Garside length of the braid, as was conjectured by Krammer. Our proof is close in spirit to Bigelow's geometric approach. The key observation is that the dual Garside length of a braid can be read off a certain labeling of its curve diagram.

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