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H 2 Extensions between Iwahori-Hecke modules for $SL_2(F)$ in characteristic $p$

Auteurs : Abdellatif, Ramla (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... structure of the pro-$p$-Iwahori-Hecke algebra results on simple Iwahori-Hecke modules comparison with mod $p$ representation theory application to representation theory: smooth duality necessary condition on central characters extensions between one-dimensional modules (Iwahori and exceptional cases) questions of the audience

Résumé : Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in which we aim to classify all non-trivial extensions between these modules and to compare them with their analogues for $p$-modular smooth representations of $SL_2(F)$ and with their Galois counterpart in the setting of the local Langlands correspondences in natural characteristic.

Codes MSC :
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
11F85 - $p$-adic theory, local fields
20C08 - Hecke algebras and their representations
20G05 - Representation theory of linear algebraic groups
22E50 - Representations of Lie and linear algebraic groups over local fields

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 16/11/16 Date de captation : 09/11/16 Collection : Research talks Format : MP4 (.mp4) - HD Durée : 00:50:39 Domaine : Lie Theory and Generalizations ; Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2016-11-09_Abdellatif.mp4 Informations sur la rencontre Nom du congrès : Representation theory of finite and p-adic groups of Lie type / Représentation des groupes de Lie finis et p-adiquesOrganisteurs Congrès : Brunat, Olivier ; Guilhot, Jérémie ; Lyle, SinéadDates : 07/11/16 - 10/11/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1504.html Citation Data DOI : 10.24350/CIRM.V.19084603 Cite this video as: Abdellatif, Ramla (2016). Extensions between Iwahori-Hecke modules for $SL_2(F)$ in characteristic $p$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19084603 URI : http://dx.doi.org/10.24350/CIRM.V.19084603

### Voir aussi

Bibliographie

1. Abdellatif, R. (2014). Classification des représentations modulo $p$ de $SL(2,F)$. Bulletin de la Société Mathématique de France, 142(3), 537-589 - http://smf4.emath.fr/en/Publications/Bulletin/142/html/smf_bull_142_537-589.php

2. Abdellatif, R. Classification of Iwahori-Hecke modules and $p$-modular representations of $SL_{2}(F)$. Submitted -

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