## Weak cuspidality and the Howe correspondence

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- by Jesua Epequin
- Represent. Theory
**26**(2022), 1080-1096 - DOI: https://doi.org/10.1090/ert/625
- Published electronically: October 14, 2022
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## Abstract:

We study the effect of the Howe correspondence on Harish-Chandra series for type I dual pairs over finite fields with odd characteristic. We define a bijection obtained from this correspondence, and enjoying the property of “having minimal unipotent support”. Finally, we examine the interaction between the Howe correspondence and weak cuspidality.## References

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## Bibliographic Information

**Jesua Epequin**- Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100190, People’s Republic of China
- MR Author ID: 1331438
- Received by editor(s): December 5, 2020
- Received by editor(s) in revised form: September 26, 2021, and June 5, 2022
- Published electronically: October 14, 2022
- Additional Notes: The author was supported by the Academy of Mathematics and Systems Science (AMSS) of the Chinese Academy of Science (CAS), and Concytec-Fondecyt-Perú (subvención Nro. 220 - 2014 - Fondecyt) during the preparation of this work.
- © Copyright 2022 American Mathematical Society
- Journal: Represent. Theory
**26**(2022), 1080-1096 - MSC (2020): Primary 20C33
- DOI: https://doi.org/10.1090/ert/625
- MathSciNet review: 4496972