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# Artin Groups and Yokonuma-Hecke Algebras

Abstract : 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.
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Article dans une revue
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621313
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Soumis le : lundi 28 mars 2022 - 10:19:20
Dernière modification le : vendredi 16 septembre 2022 - 17:30:24

### Citation

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

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