On Jiang's wavefront sets conjecture for representations in local Arthur packets
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.
Cite
@article{arxiv.2603.13465,
title = {On Jiang's wavefront sets conjecture for representations in local Arthur packets},
author = {Baiying Liu and Freydoon Shahidi},
journal= {arXiv preprint arXiv:2603.13465},
year = {2026}
}
Comments
Strengthened the main result. Comments are welcome. This note was available around 2022. Announcement of the result is available here: arXiv:2503.05343