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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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Tame supercuspidal representations of $\mathrm {GL}_n$ distinguished by orthogonal involutions
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by Jeffrey Hakim PDF
Represent. Theory 17 (2013), 120-175 Request permission

Abstract:

For a $p$-adic field $F$ of characteristic zero, the embeddings of a tame supercuspidal representation $\pi$ of $G= \textrm {GL}_n (F)$ in the space of smooth functions on the set of symmetric matrices in $G$ are determined. It is shown that the space of such embeddings is nonzero precisely when $-1$ is in the kernel of $\pi$ and, in this case, this space has dimension four. In addition, the space of $H$-invariant linear forms on the space of $\pi$ is determined whenever $H$ is an orthogonal group in $n$ variables contained in $G$.
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Additional Information
  • Jeffrey Hakim
  • Affiliation: Department of Mathematics and Statistics, American University, Washington, DC 20016
  • MR Author ID: 272088
  • Email: jhakim@american.edu
  • Received by editor(s): August 16, 2011
  • Received by editor(s) in revised form: May 11, 2012, July 22, 2012, July 25, 2012, and September 11, 2012
  • Published electronically: March 4, 2013
  • Additional Notes: The author was supported by NSF grant DMS-0854844.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 120-175
  • MSC (2010): Primary 22E50, 11F70; Secondary 11F67, 11E08, 11E81
  • DOI: https://doi.org/10.1090/S1088-4165-2013-00426-0
  • MathSciNet review: 3027804