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- W4293327265 abstract "In this paper we introduce a class of `parabolic' subgroups for the generalized braid group associated to an arbitrary irreducible complex reflection group, which maps onto the collection of parabolic subgroups of the reflection group. Except for one case, we prove that this collection forms a lattice, so that intersections of parabolic subgroups are parabolic subgroups. In particular, every element admits a parabolic closure, which is the smallest parabolic subgroup containing it. We furthermore prove that it provides a simplicial complex which generalizes the curve complex of the usual braid group. In the case of real reflection groups, this complex generalizes the one previously introduced by Cumplido, Gebhardt, Gonz'alez-Meneses and Wiest for Artin groups of spherical type. We show that it shares similar properties, and similarly conjecture its hyperbolicity." @default.
- W4293327265 created "2022-08-27" @default.
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- W4293327265 date "2022-08-25" @default.
- W4293327265 modified "2023-09-27" @default.
- W4293327265 title "Parabolic subgroups of complex braid groups I" @default.
- W4293327265 doi "https://doi.org/10.48550/arxiv.2208.11938" @default.
- W4293327265 hasPublicationYear "2022" @default.
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