Establishes reciprocity of wavefront sets and proves the Wavefront Set Conjecture for generic L-parameter representations of classical groups, determining the microlocal structure of characters via arithmetic L-data.
On Jiang's wavefront sets conjecture for representations in local Arthur packets
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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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math.RT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character
Establishes reciprocity of wavefront sets and proves the Wavefront Set Conjecture for generic L-parameter representations of classical groups, determining the microlocal structure of characters via arithmetic L-data.