Séminaires :
Séminaire Groupes Réductifs et Formes Automorphes
Equipe(s) :
fa, tn,
Responsables :
Alexis Bouthier, Francesco Lemma
Email des responsables :
alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :
Description
Orateur(s)
Jiulius Witte - Radboud Universiteit,
Titre
Buildings and local summability characters
Date
08/02/2016
Horaire
10:30 à 12:00
Diffusion
Résume
Let $\mathbb
F
$ be a non-Archimedean local field and $G$ the $\mathbb
F
$-points of a reductive group. The locally summability of the character of an admissible complex representation has been proved in the case the field $\mathbb
F
$ has characteristics $0$ by Harish-Chandra. We are currently trying to generalize this result to all non-Archimedean local fields. We get an upper-bound for the absolute value of the character in terms of the Bruhat-Tits building, using an alternative description of the character in terms of the building by Meyer and Solleveld. By a proof that uses that upper-bound, for tori $T$ containing a maximal split torus the character is locally summable on $^GT$, the $G$-orbit of $T$ under conjugation. At the end we will discuss some unsolved problems concerning the other tori regarding this approach.
Salle
Adresse
© IMJ-PRG
