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arXiv · 2409.00144

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

Asilata Bapat·Hoel Queffelec
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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 $\tilde{A_3}$, and not faithful over several finite rings in type $D_4$, using an algorithmic approach based on categorical methods that generalize Bigelow's curve strategy outside of type $A$.

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Asilata Bapat, Hoel Queffelec. 2024-08-30. Some remarks about the faithfulness of the Burau representation of Artin--Tits groups. https://arxiv.org/abs/2409.00144

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