On Jiang's wavefront sets conjecture for representations in local Arthur packets

TL;DR

This paper investigates Jiang's wavefront sets conjecture for local Arthur packets in classical groups, linking wavefront set structure to local Arthur parameters and building on recent results for split groups.

Contribution

It reduces the conjecture to properties of wavefront sets of GL representations, leveraging character identities and recent theorems for split classical groups.

Findings

Reduction of the conjecture to wavefront set properties of GL representations.

Application of character identities and matching methods.

Connection to recent results by Atobe and Ciubotaru for split groups.

Abstract

This paper serves as an attempt towards the Jiang conjecture on the upper bound nilpotent orbits in the wavefront sets of representations in local Arthur packets of quasi-split classical groups, which is a natural generalization of the well-known Shahidi conjecture, reflecting the relation between the structure of wavefront sets and the local Arthur parameters. Applying the character identities of local Arthur packets and a matching method, we reduce the study of the upper bound to certain properties of the wavefront sets of the corresponding bi-torsor representations of general linear groups, which is implied by a recent result of Atobe and Ciubotaru for split classical groups when the residue characteristic is large.