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arXiv · 2603.13465

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

Baiying Liu·Freydoon Shahidi
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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.

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Baiying Liu, Freydoon Shahidi. 2026-03-13. On Jiang's wavefront sets conjecture for representations in local Arthur packets. https://arxiv.org/abs/2603.13465

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