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SUMMARY:Ramla Abdellatif (Université de Picardie Jules Verne)
DTSTART:20201218T123000Z
DTEND:20201218T133000Z
DTSTAMP:20260416T044722Z
UID:NTRV/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTRV/10/">Re
 striction of $p$-modular representations of $p$-adic groups to minimal par
 abolic subgroups</a>\nby Ramla Abdellatif (Université de Picardie Jules V
 erne) as part of Number Theory and Representations in Valparaiso\n\n\nAbst
 ract\nGiven a prime integer $p$\, a non-archimedean local field $F$ of res
 idual characteristic $p$ and a standard Borel subgroup $P$ of $GL_{2}(F)$\
 , Pa${\\check{\\text{s}}}$k$\\overline{\\text{u}}$nas proved that the rest
 riction 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 Pa${\\check{\\text{s}}}$k$\\overline{\\text{u}}$nas heavil
 y relied on the understanding of the action of certain spherical Hecke ope
 rator and on some combinatorics specific to the $GL_{2}(F)$ case. This met
 hod can be transposed case by case to for some other quasi-split groups of
  rank $1$\, but this is not very satisfying as such. \n\nThis talk will re
 port on a joint work with J. Hauseux. Using Emerton's ordinary parts funct
 or\, we get a more uniform context which sheds a new light on Pa${\\check{
 \\text{s}}}$k$\\overline{\\text{u}}$nas' results and allows us to generali
 ze very naturally these results for arbitrary rank $1$ groups. In particul
 ar\, we prove that for such groups\, the restriction of supersingular repr
 esentations to a minimal parabolic subgroup is always irreducible.\n
LOCATION:https://researchseminars.org/talk/NTRV/10/
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