Complementary series for -adic groups. I

Author:
Allan J. Silberger

Journal:
Trans. Amer. Math. Soc. **259** (1980), 589-598

MSC:
Primary 22E50

DOI:
https://doi.org/10.1090/S0002-9947-1980-0567099-5

MathSciNet review:
567099

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Abstract: Let be a nonarchimedean local field, *G* the group of -points of a connected reductive algebraic group defined over . 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:
https://doi.org/10.1090/S0002-9947-1980-0567099-5

Keywords:
Complementary series,
unitary representations,
induced representations

Article copyright:
© Copyright 1980
American Mathematical Society