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The Arthur-Packet Support Equality for Real Reductive Groups

  • Jiawei Yang
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Abstract

Let ψ be a real Arthur parameter and let ψ2 be the unipotent parameter in a fixed Jordan decomposition. Adams, Ionov, Mason-Brown, and Vogan proved that the microlocal packet of ψ is contained in the support of the two-step Jordan induction of the packet of ψ2, and conjectured equality. We prove the reverse inclusion. The argument first passes to a sufficiently positive translate, where the relevant connected components of the ABV spaces have a common flag-variety model. Perverse devissage reduces the problem to a singular-support implication, which follows from the incidence calculation underlying the AIMV microstalk comparison. Coherent continuation for individual packet members then returns the result to the original parameter.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026arthurpacket,
  title = {{The Arthur-Packet Support Equality for Real Reductive Groups}},
  author = {Jiawei Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19197},
  eprint = {2609.19197},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19197},
}
RIS
TY  - UNPB
TI  - The Arthur-Packet Support Equality for Real Reductive Groups
AU  - Jiawei Yang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19197
UR  - https://arxiv.org/abs/2609.19197
AB  - Let ψ be a real Arthur parameter and let ψ_2 be the unipotent parameter in a fixed Jordan decomposition. Adams, Ionov, Mason-Brown, and Vogan proved that the microlocal packet of ψ is contained in the support of the two-step Jordan induction of the packet of ψ_2, and conjectured equality. We prove the reverse inclusion. The argument first passes to a sufficiently positive translate, where the relevant connected components of the ABV spaces have a common flag-variety model. Perverse devissage reduces the problem to a singular-support implication, which follows from the incidence calculation underlying the AIMV microstalk comparison. Coherent continuation for individual packet members then returns the result to the original parameter.
ER  -