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

Asilata Bapat; Hoel Queffelec

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

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arxiv 2409.00144 v1 pith:POHCFPMX submitted 2024-08-30 math.RT math.GRmath.GT

Asilata Bapat , Hoel Queffelec This is my paper · ORCID

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keywords buraugroupsrepresentationtypeartin--titsfaithfulfaithfulnessaffine

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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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A basis and Schur-Weyl duality for the loop Hecke algebra
math.RT 2025-07 conditional novelty 8.0 of 10

The loop Hecke algebra has dimension 1/2 * binom(2n,n) for z ≠ ±1, and is isomorphic to the endomorphism algebra of a tensor power for the negative half of quantum gl(1|1).

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