Towards spetses I |
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Authors: | M. Broué G. Malle J. Michel |
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Affiliation: | (1) Institut Universitaire de France, Université Paris 7, CNRS UMR 7586, Case 7012, 2 Place Jussieu, F-75251 Paris Cedex 05, France;(2) Fachbereich Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Straße 40, D-34132 Kassel, Germany;(3) UMR 7586 du CNRS, Université Paris 7, Case 7012, 2 Place Jussieu, F-75251 Paris Cedex 05, France;(4) LAMFA, CNRS UPRES-A 6119, 33 rue Saint-Leu, F-80039 Amiens Cédex 01, France |
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Abstract: | We present a formalization, using data uniquely defined at the level of the Weyl group, of the construction and combinatorial properties of unipotent character sheaves and unipotent characters for reductive algebraic groups over an algebraic closure of a finite field. This formalization extends to the case where the Weyl group is replaced by a complex reflection group, and in many cases we get families of unipotent characters for a mysterious object, a kind of reductive algebraic group with a nonreal Weyl group, the spets.In this first part, we present the general results about complex reflection groups, their associated braid groups and Hecke algebras, which will be needed later on for properties of spetses. Not all irreducible complex reflection groups will give rise to a spets (the ones which do so are called spetsial), but all of them afford properties which already allow us to generalize many of the notions attached to the Weyl groups through the approach of generic groups (see [BMM1]).To Claude Chevalley |
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