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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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Distinguished tame supercuspidal representations and odd orthogonal periods
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by Jeffrey Hakim and Joshua Lansky PDF
Represent. Theory 16 (2012), 276-316 Request permission

Abstract:

We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive $p$-adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We apply our results to study the representations of $\mathrm {GL}_n(F)$, with $n$ odd and $F$ a nonarchimedean local field, that are distinguished with respect to an orthogonal group in $n$ variables. In particular, we determine precisely when a supercuspidal representation is distinguished with respect to an orthogonal group and, if so, that the space of distinguishing linear forms has dimension one.
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Additional Information
  • Jeffrey Hakim
  • Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
  • MR Author ID: 272088
  • Email: jhakim@american.edu
  • Joshua Lansky
  • Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
  • Email: lansky@american.edu
  • Received by editor(s): March 7, 2011
  • Received by editor(s) in revised form: November 23, 2011
  • Published electronically: June 1, 2012
  • Additional Notes: Both authors were supported by NSF grant DMS-0854844.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 16 (2012), 276-316
  • MSC (2010): Primary 22E50, 11F70; Secondary 11F67, 11E08, 11E81
  • DOI: https://doi.org/10.1090/S1088-4165-2012-00418-6
  • MathSciNet review: 2925798