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.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.