Ramla Abdellatif: Restriction of p-modular representations of p-adic groups to minimal parabolic subgroups
Time: Wed 2020-02-26 11.00 - 12.00
Lecturer: Ramla Abdellatif, Université de Picardie Jules Verne
Location: KTH, F11
Given a prime integer p, a non-archimedean local field F of residual characteristic p and a standard Borel subgroup P of GL2(F), Paskunas proved that the restriction to P of (irreducible) smooth representations of GL2(F) over F_p encodes a lot of information about the full representation of GL2(F) and that it leads to useful statement about p-adic representations of GL2(F). Nevertheless, the methods used at that time by Paskunas heavily relied on the understanding of the action of certain spherical Hecke operator and on some combinatorics specific to the GL2(F) case. This method can be transposed case by case to some other quasi-split groups of rank 1, but this is not very satisfying as such.
This talk will report on a joint work with J. Hauseux. Using Emerton’s ordinary parts functor, we get a more uniform context which sheds a new light on Paskunas’ results and allows us to generalize very naturally these results for arbitrary rank 1 groups. In particular, we prove that for such groups, the restriction of supersingular representations to a minimal parabolic subgroup is always irreducible.