Some Unipotent Arthur Packets for Reductive p-adic Groups I

Abstract

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.

Jiang’s conjecture and Fibers of the Barbasch-Vogan duality

“…We remark that recent work of Ciubotaru-Mason-Brown-Okada ( [6][7][8]) and Waldspurger ([27]), combining the closure relation result of [10], imply that Jiang's conjecture 1.3 holds for any local Arthur parameter ψ of Sp 2n (F ) or split SO 2n+1 (F ) which is trivial on W F . For more discussion, see [11].…”