Menu Fermer

Distinction of the Steinberg representation with respect to split symmetric subgroups

Orateur : Guy Shtotland
Établissement : Ben-Gurion University of the Negev ()
Dates : 2025-03-20 – 2025-03-20
Heures : 14:00 – 14:00
Lieu : Salle 0-6

Résumé :
We study the distinction of the Steinberg representation of a split p adic group G with respect to a split symmetric subgroup H. We relate this problem to the problem of determining the existence of a non zero harmonic function on a certain hyper graph related to X=G/H. We show that the Steinberg representation is distinguished only if X is quasi-split and that GL_{2n+1}/GL_{n}xGL_{n+1} is essentially the only example where X is quasi-split but the Steinberg representation isn’t distinguished. As a corollary we obtain a proof of the relative local Langlands conjecture for the Steinberg representation, we show that the Steinberg representation is distinguished if and only if its parameter factors through the dual group of X.

Laisser un commentaire

Votre adresse e-mail ne sera pas publiée. Les champs obligatoires sont indiqués avec *