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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Complementary series for $ p$-adic groups. I


Author: Allan J. Silberger
Journal: Trans. Amer. Math. Soc. 259 (1980), 589-598
MSC: Primary 22E50
MathSciNet review: 567099
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Abstract: Let $ \Omega $ be a nonarchimedean local field, G the group of $ \Omega $-points of a connected reductive algebraic group defined over $ \Omega $. This paper establishes that to each zero of the Plancherel measure of G one can associate complementary series. Our result is the analogue for p-adic groups of a similar statement, announced separately by Knapp-Stein and Harish-Chandra, for real groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0567099-5
PII: S 0002-9947(1980)0567099-5
Keywords: Complementary series, unitary representations, induced representations
Article copyright: © Copyright 1980 American Mathematical Society