Restriction of p-modular Representations of p-adic Groups to Minimal Parabolic Subgroups

par Ramla Abdellatif (Université de Picardie Jules Verne)

mercredi 1 déc. 2021, 14:30 → 15:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire de géométrie arithmétique

Given a prime integer p, a non-archimedean local field F of residual characteristic p and a standard Borel subgroup P of ${GL}_{2} (F)$, Paškūnas proved that the restriction to P of (irreducible) smooth representations of ${GL}_{2} (F)$ over $\overline{\mathbb F}_p$ encodes a lot of information about the full representation of ${GL}_{2} (F)$ and that it leads to useful statement about p-adic representations of ${GL}_{2} (F)$. Nevertheless, the methods used at that time by Paškūnas heavily relied on the understanding of the action of certain spherical Hecke operator and on some combinatorics specific to the ${GL}_{2} (F)$ case. This method can be transposed case by case to for some other quasi-split groups of rank 1, but this is not very satisfying as such.

This talk will report on a joint work with J. Hauseux. Using Emerton's ordinary parts functor, we get a more uniform context which shed a new light on Paškūnas' results and allows us to generalize very naturally these results for arbitrary rank 1 groups. In particular, we prove that for such groups, the restriction of supersingular representations to a minimal parabolic subgroup is always irreducible.

==================================================================

IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe seminaire_mathematique PRENOM NOM"
(indiquez vos propres prénom et nom) et laissez le corps du message vide.