# Séminaires : Séminaire Groupes, Représentations et Géométrie

 Equipe(s) : gr, Responsables : A. Brochier, O. Brunat, J.-Y. Charbonnel, O. Dudas, E. Letellier, D. Juteau, M. Varagnolo, E. Vasserot Email des responsables : Adrien Brochier , Olivier Brunat , Jean-Yves Charbonnel , Olivier Dudas , Emmanuel Letellier , Daniel Juteau , Michela Varagnolo , Eric Vasserot Salle : salle 2015, 2em étage, Adresse : Sophie Germain Description

 Orateur(s) Dan CIUBOTARU - Oxford University, Titre Dirac operators for graded affine Hecke algebras and rational Cherednik algebras Date 22/01/2016 Horaire 10:30 à 11:30 Diffusion Résume We define uniformly the notions of Dirac operators and Dirac cohomology in the framework of the Hecke algebras introduced by Drinfeld (1986). In particular, these constructions apply to Lusztig's graded affine Hecke algebras, where we recover results previously obtained in joint work with D. Barbasch and P. Trapa, and to rational Cherednik algebras. An important feature of this theory is the existence of a Dirac morphism between the irreducible representations of certain double covers of reflection groups and the central characters of the algebra. I will explain the relation between this morphism and Springer theory for finite Weyl groups in the graded affine Hecke algebra case (joint, in part, with X. He), and Lusztig's two sided cells for finite reflection groups in the case of rational Cherednik algebra at $t=0$. Salle salle 2015, 2em étage, Adresse Sophie Germain