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Extensions between Iwahori-Hecke modules for $SL_2(F)$ in characteristic $p$
Post-edited
Authors : Abdellatif, Ramla (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 16/11/16 Conference Date : 09/11/16 Subseries : Research talks arXiv category : Group Theory Mathematical Area(s) : Lie Theory and Generalizations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:50:39 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-11-09_Abdellatif.mp4 
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Information on the Event
Event Title : Representation theory of finite and p-adic groups of Lie type / Représentation des groupes de Lie finis et p-adiquesEvent Organizers : Brunat, Olivier ; Guilhot, Jérémie ; Lyle, Sinéad Dates : 07/11/16 - 10/11/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1504.html
Citation Data
DOI : 10.24350/CIRM.V.19084603Cite 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 |
See Also
- [Multi angle] Quasisemisimple classes / Author of the conference Michel, Jean.
Bibliography
- 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
- Abdellatif, R. Classification of Iwahori-Hecke modules and $p$-modular representations of $SL_{2}(F)$. Submitted -
