| Speaker: | Ramla Abdellatif (Amiens University - IMAR) |
|---|---|
| Title: | Searching for a $p$-modular Shimura-Langlands correspondence for the $p$-adic metaplectic $\widetilde{\mathrm{SL}}_{2}$ |
| Date (JST): | Thu, Oct 30, 2025, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
The first part of my talk aims to introduce the context of my primary research topic, namely $p$-modular representations of $p$-adic groups, where $p$ is a fixed prime integer, as well as a current state of the art in the field. It is aimed at a large audience and do not require specific knowledge in the topic. The second part of my talk reports on a collaborative work with Dr. Purkait (Institute of Science Tokyo) on $p$-modular representations of $\widetilde{\mathrm{SL}}_{2}(F)$, the $p$-adic double cover of the special linear group $\mathrm{SL}_{2}(F)$, with $F$ a finite extension of the field of $p$-adic numbers. It presents some of the results we proved about the Iwahori-Hecke algebras associated with this group, as well as a classification of their simple modules and the relations that bind them to the $p$-modular representation theory of $\widetilde{\mathrm{SL}}_{2}(F)$. |
