On the reality of complex reflection groups (and their associated Hecke algebras)
Maria Chlouveraki (Laboratoire de Mathématiques de Versailles)
Wednesday 10th March 16:00-17:00 online (zoom)
Iwahori-Hecke algebras associated to Weyl groups appear naturally as endomorphism algebras in the representation theory of finite reductive groups. Weyl groups are real reflection groups, which in turn are particular cases of complex reflection groups. Hecke algebras associated to complex reflection groups were introduced by Broué, Malle and Rouquier 20 years ago, but many of the properties of real Hecke algebras were simply conjectured in the complex case. In this talk, we are going to discuss the most fundamental of these conjectures, their state of art and our contributions to it.