Non-admissible irreducible representations of $p$-adic $\mathrm {GL}_{n}$ in characteristic $p$
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- by Eknath Ghate, Daniel Le and Mihir Sheth;
- Represent. Theory 27 (2023), 1088-1101
- DOI: https://doi.org/10.1090/ert/660
- Published electronically: November 6, 2023
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Abstract:
Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb {F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm {GL}_2(F)$ defined over the residue field of $F$ extending the earlier results of the authors for $F$ unramified over $\mathbb {Q}_{p}$. This construction uses the theory of diagrams of Breuil and Pašk$\bar {\mathrm {u}}$nas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of $\mathrm {GL}_n(F)$ for $n>2$.References
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Bibliographic Information
- Eknath Ghate
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400005, India
- ORCID: 0000-0003-4780-5191
- Email: eghate@math.tifr.res.in
- Daniel Le
- Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
- MR Author ID: 900375
- ORCID: 0000-0002-0220-6366
- Email: ledt@purdue.edu
- Mihir Sheth
- Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
- MR Author ID: 1400783
- Email: mihirsheth@iisc.ac.in
- Received by editor(s): December 21, 2022
- Received by editor(s) in revised form: March 2, 2023, April 23, 2023, and August 10, 2023
- Published electronically: November 6, 2023
- Additional Notes: During this work, the second-named author was supported by a start-up grant from Purdue University, and the third-named author was supported by the Raman Postdoctoral Fellowship from Indian Institute of Science, Bangalore.
- © Copyright 2023 American Mathematical Society
- Journal: Represent. Theory 27 (2023), 1088-1101
- MSC (2020): Primary 22E50, 11S37
- DOI: https://doi.org/10.1090/ert/660
- MathSciNet review: 4664337