## On the Jacquet Conjecture on the local converse problem for $p$-adic $\mathrm {GL}_N$

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- by Moshe Adrian, Baiying Liu, Shaun Stevens and Peng Xu
- Represent. Theory
**20**(2016), 1-13 - DOI: https://doi.org/10.1090/ert/476
- Published electronically: January 27, 2016
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## Abstract:

Based on previous results of Jiang, Nien and the third-named author, we prove that any two*minimax*unitarizable supercuspidals of $p$-adic $\mathrm {GL}_N$ that have the same depth and central character admit a

*special pair*of Whittaker functions. As a corollary of our result, we prove Jacquetโs conjecture on the local converse problem for $\mathrm {GL}_N$, when $N$ is prime.

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## Bibliographic Information

**Moshe Adrian**- Affiliation: Department of Mathematics, Queens College, Queens, New York 11367-1597
- Email: moshe.adrian@qc.cuny.edu
**Baiying Liu**- Affiliation: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
- MR Author ID: 953254
- Email: liu@ias.edu
**Shaun Stevens**- Affiliation: School of Mathematics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom
- MR Author ID: 678092
- Email: Shaun.Stevens@uea.ac.uk
**Peng Xu**- Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 1099916
- Email: Peng.Xu@warwick.ac.uk
- Received by editor(s): March 4, 2015
- Received by editor(s) in revised form: October 8, 2015
- Published electronically: January 27, 2016
- Additional Notes: The second author was supported in part by NSF Grant DMS-1302122, and in part by a postdoc research fund from Department of Mathematics, University of Utah

The third and fourth authors were supported by the Engineering and Physical Sciences Research Council (grant EP/H00534X/1) - © Copyright 2016 American Mathematical Society
- Journal: Represent. Theory
**20**(2016), 1-13 - MSC (2010): Primary 11S70, 22E50; Secondary 11F85, 22E55
- DOI: https://doi.org/10.1090/ert/476
- MathSciNet review: 3452696