Non-basic rigid packets for discrete L-parametersMPIM

by Peter Dillery (University of Maryland)

Friday Jan 17, 2025, 2:05 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Arithmetic Geometry and Representation Theory Research Seminar: https://www.math.uni-bonn.de/ag/alggeom/AGaRTseminar

We formulate a new version of the local Langlands correspondence for discrete L-parameters which involves (Weyl orbits of) packets of representations of all twisted Levi subgroups of a connected reductive group G through which a given parameter factors and prove that this version of the correspondence is true if one assumes the pre-existing local Langlands conjectures. Twisted Levi subgroups are crucial objects in the study of supercuspidal representations; this work is a step towards deepening the relationship between the representation theory of p-adic groups and the Langlands correspondence. This talk will also serve as a rough introduction to the refined local Langlands correspondence (and its generalizations). This is joint work with David Schwein.