Artin Groups and Yokonuma-Hecke Algebras

作者：Marin Ivan^*

来源：International Mathematics Research Notices, 2018, (13): 4022-4062.

DOI：10.1093/imrn/rnx007

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.

• 出版日期2018-7