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The $ SL(2)$-type and base change


Authors: Omer Offen and Eitan Sayag
Journal: Represent. Theory 13 (2009), 228-235
MSC (2000): Primary 22E50; Secondary 11S37
DOI: https://doi.org/10.1090/S1088-4165-09-00353-7
Published electronically: June 23, 2009
MathSciNet review: 2515933
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Abstract: 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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Additional 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

DOI: https://doi.org/10.1090/S1088-4165-09-00353-7
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)
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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