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Transactions of the American Mathematical Society

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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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Keywords: Complementary series, unitary representations, induced representations
Article copyright: © Copyright 1980 American Mathematical Society