## Complementary series for $p$-adic groups. I

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- by Allan J. Silberger PDF
- Trans. Amer. Math. Soc.
**259**(1980), 589-598 Request permission

## 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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*Complementary series representations of*${\text {GL}}(2,\,D)$,

*where D is a central division algebra over a non-archimedean local field*, Notices Amer. Math. Soc.

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## Additional Information

- © Copyright 1980 American Mathematical Society
- 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