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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Tame supercuspidal representations of $\mathrm {GL}_n$ distinguished by orthogonal involutions
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by Jeffrey Hakim
Represent. Theory 17 (2013), 120-175
Published electronically: March 4, 2013


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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Bibliographic Information
  • Jeffrey Hakim
  • Affiliation: Department of Mathematics and Statistics, American University, Washington, DC 20016
  • MR Author ID: 272088
  • Email:
  • 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:
  • MathSciNet review: 3027804