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Characterizations of the Burau representation. (Charactérisations de la représentation de Burau.) (French) Zbl 1064.20042

Summary: This paper is devoted to characterizations of the (reduced) Burau representation of the Artin braid group, in terms of rigid local systems. We prove that the Burau representation is the only representation of the Hecke algebra for which some local system associated to every linear representation of the braid group is irreducible and rigid in the sense of Katz. We also use previous results to give a characterization of the corresponding Knizhnik-Zamolodchikov system.

MSC:

20F36 Braid groups; Artin groups
20C15 Ordinary representations and characters
20C08 Hecke algebras and their representations
32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)
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References:

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