Mod-p representations of p-adic metaplectic groups

Seminar
Speaker
Dr. Laura Peskin (Weizmann Institute of Science)
Date
06/04/2016 - 11:30 - 10:30Add to Calendar 2016-04-06 10:30:00 2016-04-06 11:30:00 Mod-p representations of p-adic metaplectic groups Let F be a p-adic field. The irreducible admissible mod-p representations of a connected reductive group over F have recently been classified up to supercuspidals by Abe-Henniart-Herzig-Vigneras, building on a method introduced by Herzig in 2011. Their classification is part of an effort to formulate mod-p local Langlands correspondences. The complex representations of certain nonlinear covers of p-adic reductive groups play an interesting role in the classical LLC, and it is natural to ask whether this is also true in the mod-p setting. As a first step, I’ll explain how to modify Herzig’s method in order to classify irreducible admissible genuine mod-p representations of the metaplectic double cover of Sp_{2n}(F). The main consequence of the classification is that parabolically induced genuine mod-p representations are irreducible in the metaplectic case more often than in the reductive case; in particular, all parabolically induced genuine representations of the metaplectic cover of SL_{2}(F) are irreducible. This is joint work with Karol Koziol.  Third floor seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

Let F be a p-adic field. The irreducible admissible mod-p representations of a connected reductive group over F have recently been classified up to supercuspidals by Abe-Henniart-Herzig-Vigneras, building on a method introduced by Herzig in 2011. Their classification is part of an effort to formulate mod-p local Langlands correspondences. The complex representations of certain nonlinear covers of p-adic reductive groups play an interesting role in the classical LLC, and it is natural to ask whether this is also true in the mod-p setting. As a first step, I’ll explain how to modify Herzig’s method in order to classify irreducible admissible genuine mod-p representations of the metaplectic double cover of Sp_{2n}(F). The main consequence of the classification is that parabolically induced genuine mod-p representations are irreducible in the metaplectic case more often than in the reductive case; in particular, all parabolically induced genuine representations of the metaplectic cover of SL_{2}(F) are irreducible. This is joint work with Karol Koziol. 

Last Updated Date : 29/03/2016