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Multiplicity One for Five Strongly Tempered Spherical Varieties

  • Yuxuan Ge
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Abstract

Let F be a non-Archimedean local field of characteristic zero. We prove multiplicity one for every irreducible smooth admissible representation in the split forms of Wan-Zhang Models 6-10. Combining the Gelfand-Kazhdan method with nilpotent-wavefront restrictions on Bernstein-finite equivariant distributions, we establish the required symmetries through rational orbit analysis, parabolic descent, stabilizer characters, and conormal arguments. The type-D6 analysis treats both the vector-similitude group of Model 9 and the semispin form arising in the exceptional E7 model. For Model 10, the distribution theorem gives a product bound for periods; the individual multiplicity bound follows from Langlands classification and a vanishing theorem for standard modules induced from nongeneric tempered data on the maximal E6 Levi.

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Cite

BibTeXRIS
BibTeX
@misc{ge2026multiplicity,
  title = {{Multiplicity One for Five Strongly Tempered Spherical Varieties}},
  author = {Yuxuan Ge},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17888},
  eprint = {2610.17888},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17888},
}
RIS
TY  - UNPB
TI  - Multiplicity One for Five Strongly Tempered Spherical Varieties
AU  - Yuxuan Ge
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17888
UR  - https://arxiv.org/abs/2610.17888
AB  - Let F be a non-Archimedean local field of characteristic zero. We prove multiplicity one for every irreducible smooth admissible representation in the split forms of Wan-Zhang Models 6-10. Combining the Gelfand-Kazhdan method with nilpotent-wavefront restrictions on Bernstein-finite equivariant distributions, we establish the required symmetries through rational orbit analysis, parabolic descent, stabilizer characters, and conormal arguments. The type-D_6 analysis treats both the vector-similitude group of Model 9 and the semispin form arising in the exceptional E_7 model. For Model 10, the distribution theorem gives a product bound for periods; the individual multiplicity bound follows from Langlands classification and a vanishing theorem for standard modules induced from nongeneric tempered data on the maximal E_6 Levi.
ER  -