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Multiplicity One Property for Archimedean Theta Correspondence

  • Zhibin Geng
  • Kaidi Wu
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Abstract

For any archimedean reductive dual pair, we prove that the Jordan-Hölder multiplicity of the small theta lift in the full theta lift is one. The main input is an equality between the multiplicities of the lowest degree K-types in the full and small theta lifts. We also deduce a new description of the archimedean theta correspondence in terms of lowest degree K-types.

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Cite

BibTeXRIS
BibTeX
@misc{geng2026multiplicity,
  title = {{Multiplicity One Property for Archimedean Theta Correspondence}},
  author = {Zhibin Geng and Kaidi Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26630},
  eprint = {2609.26630},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26630},
}
RIS
TY  - UNPB
TI  - Multiplicity One Property for Archimedean Theta Correspondence
AU  - Zhibin Geng
AU  - Kaidi Wu
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26630
UR  - https://arxiv.org/abs/2609.26630
AB  - For any archimedean reductive dual pair, we prove that the Jordan-Hölder multiplicity of the small theta lift in the full theta lift is one. The main input is an equality between the multiplicities of the lowest degree K-types in the full and small theta lifts. We also deduce a new description of the archimedean theta correspondence in terms of lowest degree K-types.
ER  -