Graded Hecke Algebras for Disconnected Reductive Groups. - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2018

Graded Hecke Algebras for Disconnected Reductive Groups.

Résumé

We introduce graded Hecke algebras H based on a (possibly disconnected) complex reductive group G and a cuspidal local system L on a unipotent orbit of a Levi subgroup M of G. These generalize the graded Hecke algebras defined and investigated by Lusztig for connected G. We develop the representation theory of the algebras H. obtaining complete and canonical parametrizations of the irreducible, the irreducible tempered and the discrete series representations. All the modules are constructed in terms of perverse sheaves and equivariant homology, relying on work of Lusztig. The parameters come directly from the data (G, M, L) and they are closely related to Langlands parameters. Our main motivation for considering these graded Hecke algebras is that the space of irreducible H-representations is canonically in bijection with a certain set of "logarithms" of enhanced L-parameters. Therefore we expect these algebras to play a role in the local Langlands program. We will make their relation with the local Langlands correspondence, which goes via affine Hecke algebras, precise in a sequel to this paper.
Fichier principal
Vignette du fichier
1607.02713.pdf (627.86 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02343591 , version 1 (02-11-2019)

Identifiants

Citer

Anne-Marie Aubert, Ahmed Moussaoui, Maarten Solleveld. Graded Hecke Algebras for Disconnected Reductive Groups.. Müller, Werner, Shin, Sug Woo, Templier, Nicolas. Geometric aspects of the trace formula, Springer; Springer International Publishing, p23-84, 2018, Simons Symposia, 978-3-319-94833-1. ⟨10.1007/978-3-319-94833-1_2⟩. ⟨hal-02343591⟩
99 Consultations
59 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More