## Intertwining maps between $p$-adic principal series of $p$-adic groups

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- by Dubravka Ban and Joseph Hundley
- Represent. Theory
**25**(2021), 975-993 - DOI: https://doi.org/10.1090/ert/571
- Published electronically: December 1, 2021
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## Abstract:

In this paper we study $p$-adic principal series representation of a $p$-adic group $G$ as a module over the maximal compact subgroup $G_0$. We show that there are no non-trivial $G_0$-intertwining maps between principal series representations attached to characters whose restrictions to the torus of $G_0$ are distinct, and there are no non-scalar endomorphisms of a fixed principal series representation. This is surprising when compared with another result which we prove: that a principal series representation may contain infinitely many closed $G_0$-invariant subspaces. As for the proof, we work mainly in the setting of Iwasawa modules, and deduce results about $G_0$-representations by duality.## References

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## Bibliographic Information

**Dubravka Ban**- Affiliation: School of Mathematical and Statistical Sciences, 1245 Lincoln Drive, Southern Illinois University, Carbondale, Illinois 62901
- MR Author ID: 658785
- Email: dban@siu.edu
**Joseph Hundley**- Affiliation: Department of Mathematics, 244 Mathematics Building, University at Buffalo, Buffalo, New York 14260-2900
- MR Author ID: 746477
- Email: jahundle@buffalo.edu
- Received by editor(s): May 2, 2020
- Received by editor(s) in revised form: December 11, 2020
- Published electronically: December 1, 2021
- Additional Notes: The work on this project was partially supported by Simons Foundation Collaboration Grant 428319
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory
**25**(2021), 975-993 - MSC (2020): Primary 22E50
- DOI: https://doi.org/10.1090/ert/571
- MathSciNet review: 4346019