Some Unipotent Arthur Packets for Reductive p-adic Groups I

Dan Ciubotaru, Lucas Mason-Brown, Emile Okada

Published 2021-12-29, updated 2022-03-14Version 3

We consider Arthur's conjectures for split reductive $p$-adic groups from the point of view of the wavefront set, a fundamental invariant arising from the Harish-Chandra-Howe local character expansion of an admissible representation. We prove a precise formula for the wavefront set of an irreducible Iwahori-spherical representation with `real infinitesimal character' and determine a lower bound for this invariant in terms of the Kazhdan-Lusztig parameters. We define certain unipotent Arthur packets consisting of representations with minimal allowable wavefront sets, and we prove that their Iwahori-spherical constituents are the Aubert-Zelevinsky duals of tempered representations.