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- W4292238968 abstract "We define a representation of the Artin groups of type ADE by monodromy of generalized KZ-systems which is shown to be isomorphic to the generalized Krammer representation originally defined by A.M. Cohen and D. Wales, and independantly by F. Digne. It follows that all pure Artin groups of spherical type are residually torsion-free nilpotent, hence (bi-)orderable. Using that construction we show that these irreducible representations are Zariski-dense in the corresponding general linear group. It follows that all irreducible Artin groups of spherical type can be embedded as Zariski-dense subgroups of some general linear group. As group-theoretical applications we prove properties of non-decomposition in direct products for several subgroups of Artin groups, and a generalization in arbitrary types of a celebrated property of D. Long for the braid groups. We also determine the Frattini and Fitting subgroups and discuss unitarity properties of the representations." @default.
- W4292238968 created "2022-08-19" @default.
- W4292238968 creator A5003241846 @default.
- W4292238968 date "2005-04-07" @default.
- W4292238968 modified "2023-10-18" @default.
- W4292238968 title "Sur les representations de Krammer generiques" @default.
- W4292238968 doi "https://doi.org/10.48550/arxiv.math/0504143" @default.
- W4292238968 hasPublicationYear "2005" @default.
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