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On Irreducibility and Multiplicity One Property for Non-Archimedean Type-II Theta Lifting

  • Kaidi Wu
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Abstract

We establish a multiplicity-one refinement of the non-archimedean type-II Howe correspondence: whenever the small theta lift is non-zero, it occurs in the big theta lift with Jordan-Hölder multiplicity one. Furthermore, we apply this result alongside the Godement-Jacquet zeta integral to compute big theta lift for Arthur-type representations. Based on these computations, we also propose a conjecture regarding the irreducibility of the big theta lift.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026irreducibility,
  title = {{On Irreducibility and Multiplicity One Property for Non-Archimedean Type-II Theta Lifting}},
  author = {Kaidi Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39683},
  eprint = {2609.39683},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39683},
}
RIS
TY  - UNPB
TI  - On Irreducibility and Multiplicity One Property for Non-Archimedean Type-II Theta Lifting
AU  - Kaidi Wu
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39683
UR  - https://arxiv.org/abs/2609.39683
AB  - We establish a multiplicity-one refinement of the non-archimedean type-II Howe correspondence: whenever the small theta lift is non-zero, it occurs in the big theta lift with Jordan-Hölder multiplicity one. Furthermore, we apply this result alongside the Godement-Jacquet zeta integral to compute big theta lift for Arthur-type representations. Based on these computations, we also propose a conjecture regarding the irreducibility of the big theta lift.
ER  -