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The intersection of local Arthur packets for even orthogonal groups and applications

  • Alexander Hazeltine
  • Baiying Liu
  • Chi-Heng Lo
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Abstract

We give algorithms to explicitly compute local Arthur packets and their intersections for even orthogonal groups Gn over p-adic fields using extended multi-segments. In addition, we provide an algorithm which determines whether a representation of Gn lies in a local Arthur packet. As applications, these results are used to identify distinguished parameters, prove the closure ordering conjecture, the enhanced Shahidi conjecture, the weak local Arthur packet conjecture, and the good parity unitary dual conjecture for Gn.

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Cite

BibTeXRIS
BibTeX
@misc{hazeltine2026intersection,
  title = {{The intersection of local Arthur packets for even orthogonal groups and applications}},
  author = {Alexander Hazeltine and Baiying Liu and Chi-Heng Lo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27261},
  eprint = {2609.27261},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27261},
}
RIS
TY  - UNPB
TI  - The intersection of local Arthur packets for even orthogonal groups and applications
AU  - Alexander Hazeltine
AU  - Baiying Liu
AU  - Chi-Heng Lo
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27261
UR  - https://arxiv.org/abs/2609.27261
AB  - We give algorithms to explicitly compute local Arthur packets and their intersections for even orthogonal groups G_n over p-adic fields using extended multi-segments. In addition, we provide an algorithm which determines whether a representation of G_n lies in a local Arthur packet. As applications, these results are used to identify distinguished parameters, prove the closure ordering conjecture, the enhanced Shahidi conjecture, the weak local Arthur packet conjecture, and the good parity unitary dual conjecture for G_n.
ER  -