The Jiang conjecture on the wavefront sets of local Arthur packets

2025/03/07 by Baiying Liu, Freydoon Shahidi, Liu, Baiying +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Mathematical Analysis and Transform Methods #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2503.05343

Abstract

This is a report on the progress made on a conjecture of Jiang on the upper bound nilpotent orbits in the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of the Shahidi conjecture. We partially prove this conjecture, confirming the relation between the structure of wave front sets and the local Arthur parameters. Under certain assumptions, we also prove the enhanced Shahidi conjecture, which states that local Arthur packets are tempered if and only if they have generic members.

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• Micro-packets containing generic representations

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