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) Vytautas PASKUNAS - Université de Bielefeld,
Titre On the restriction of mod p and p-adic representations of $GL_2(F)$ to a Borel subgroup
Horaire14:00 à 15:00
RésumeLet $F$ be a non-Archimedean local field and let $p$ be the residual characteristic of $F$. Let $G=GL_2(F)$ and let $P$ be a Borel subgroup of $G$. In this paper we study the restriction of smooth irreducible representations of $G$ on $E$-vector spaces to $P$, where $E$ is an algebraically closed field of characteristic $p$. We show that in a certain sense $P$ controls the representation theory of $G$. We then extend our results to smooth $O_K[G]$- modules of finite length and unitary $K$-Banach space representations of $G$, where $O_K$ is the ring of integers of a complete discretely valued field $K$, with residue field $E$.