Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Cong Xue
Email des responsables : alexis.bouthier@imj-prg.fr, cong.xue@imj-prg.fr
Salle :
Adresse :

Orateur(s) Kam-Fai Tam - McMaster University,
Titre Endoscopic classification of essentially tame supercuspidal representations for quasi-split classical groups
Horaire10:30 à 12:00
Let $\mathbfG$ be a quasi-split classical group (special orthogonal, symplectic, unitary) over a $p$-adic field of odd residual characteristic. We describe the endoscopic classification, proved by Arthur and Mok, of certain supercuspidal representations and their L-packets of $\mathbfG$. These representations, whose inducing types can be described by the theory of Bushnell-Kutzko, Stevens, or Yu, correspond to Langlands parameters related to characters of elliptic maximal tori of $\mathbfG$, under some regularity and tameness conditions.

In order to describe this representation-character correspondence explicitly, we associate to each character another character defined on the same torus, called an amending character in this talk. These amending characters play a similar role as the Bushnell-Henniart rectifying characters in the essentially tame local Langlands correspondence for general linear groups, where both kinds of characters carry information about the inducing types. For classical groups, our amending characters further carry information about the embeddings of the elliptic maximal tori into $\mathbfG$.