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 :

Orateur(s) Jiulius Witte - Radboud Universiteit,
Titre Buildings and local summability characters
Horaire10:30 à 12:00
Let $\mathbbF$ be a non-Archimedean local field and $G$ the $\mathbbF$-points of a reductive group. The locally summability of the character of an admissible complex representation has been proved in the case the field $\mathbbF$ 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.