MIT Lie Groups Seminar
Wednesday, September 21, 2022 at 4:00pm to 5:00pm
Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139
Title: Wavefront sets and unipotent representations of p-adic groups
Abstract: An important invariant for admissible representations of reductive p-adic groups is the wavefront set, the collection of the maximal nilpotent orbits in the support of the orbital integrals that occur in the Harish-Chandra-Howe local character expansion. We compute the geometric and Okada's canonical unramified wavefront sets for representations in Lusztig's category of unipotent reduction for a split group in terms of the Kazhdan-Lusztig parameters. We use this calculation to give a new characterisation of the anti-tempered unipotent Arthur packets. Another interesting consequence is that the geometric wavefront set of a unipotent supercuspidal representation uniquely determines the nilpotent part of the Langlands parameter; this is an extension to p-adic groups of Lusztig's result for unipotent representations of finite groups of Lie type. The talk is based on joint work with Lucas Mason-Brown and Emile Okada.