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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The $SL(2)$-type and base change
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by Omer Offen and Eitan Sayag
Represent. Theory 13 (2009), 228-235
Published electronically: June 23, 2009


The $SL(2)$-type of any smooth, irreducible and unitarizable representation of $GL_n$ over a $p$-adic field was defined by Venkatesh. We provide a natural way to extend the definition to all smooth and irreducible representations. For unitarizable representations we show that the $SL(2)$-type of a representation is preserved under the base change with respect to any finite extension. The Klyachko model of a smooth, irreducible and unitarizable representation $\pi$ of $GL_n$ depends only on the $SL(2)$-type of $\pi$. As a consequence we observe that the Klyachko model of $\pi$ and of its base change are of the same type.
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Bibliographic Information
  • Omer Offen
  • Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000 Israel
  • Eitan Sayag
  • Affiliation: Department of Mathematics, Ben Gurion University, Be’er Sheva, 84105 Israel
  • Received by editor(s): August 25, 2008
  • Received by editor(s) in revised form: April 12, 2009
  • Published electronically: June 23, 2009
  • Additional Notes: In this research the first named author is supported by The Israel Science Foundation (grant No. 88/08)
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 13 (2009), 228-235
  • MSC (2000): Primary 22E50; Secondary 11S37
  • DOI:
  • MathSciNet review: 2515933