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Article Dans Une Revue International Mathematics Research Notices Année : 2018

Artin Groups and Yokonuma-Hecke Algebras

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Résumé

We attach to every Coxeter system (W, S), an extension C-W of the corresponding Iwahori-Hecke algebra. We construct a 1-parameter family of (generically surjective) morphisms from the group algebra of the corresponding Artin group onto C-W. When W is finite, we prove that this algebra is a free module of finite rank which is generically semisimple. When W is the Weyl group of a Chevalley group, C-W naturally maps to the associated Yokonuma-Hecke algebra. When W = S-n this algebra can be identified with a diagram algebra called the algebra of ``braids and ties''. The image of the usual braid group in this case is investigated. Finally, we generalize our construction to finite complex reflection groups, thus extending the Broue-Malle-Rouquier construction of a generalized Hecke algebra attached to these groups.

Dates et versions

hal-03621313 , version 1 (28-03-2022)

Identifiants

Citer

Ivan Marin. Artin Groups and Yokonuma-Hecke Algebras. International Mathematics Research Notices, 2018, 2018 (13), pp.4022-4062. ⟨10.1093/imrn/rnx007⟩. ⟨hal-03621313⟩
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