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Article Dans Une Revue International Mathematics Research Notices Année : 2018

## Artin Groups and Yokonuma-Hecke Algebras

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Ivan Marin
• Fonction : Auteur
• PersonId : 1015638
• IdRef : 137963114

#### 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.

#### Domaines

Mathématiques [math]

### Dates et versions

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

### Identifiants

• HAL Id : hal-03621313 , version 1
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• DOI :

### 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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