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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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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 PDF
Represent. Theory 20 (2016), 1-13 Request permission


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 Jacquetโ€™s conjecture on the local converse problem for $\mathrm {GL}_N$, when $N$ is prime.
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Additional Information
  • Moshe Adrian
  • Affiliation: Department of Mathematics, Queens College, Queens, New York 11367-1597
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  • Baiying Liu
  • Affiliation: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
  • MR Author ID: 953254
  • Email:
  • Shaun Stevens
  • Affiliation: School of Mathematics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom
  • MR Author ID: 678092
  • Email:
  • Peng Xu
  • Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
  • MR Author ID: 1099916
  • Email:
  • 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:
  • MathSciNet review: 3452696