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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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https://hal-u-picardie.archives-ouvertes.fr/hal-03621313
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Soumis le : lundi 28 mars 2022 - 10:19:20
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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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