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15 May 2002 Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
Hee Oh
Duke Math. J. 113(1): 133-192 (15 May 2002). DOI: 10.1215/S0012-7094-02-11314-3

Abstract

Let $k$ be a local field of characteristic not $2$, and let $G$ be the group of $k$-rational points of a connected reductive linear algebraic group defined over $k$ with a simple derived group of $k$-rank at least $2$. We construct new uniform pointwise bounds for the matrix coefficients of all infinite-dimensional irreducible unitary representations of $G$. These bounds turn out to be optimal for ${\rm SL}\sb n(k), n\geq 3$, and ${\rm Sp}\sb {2n}(k),n\geq 2$. As an application, we discuss a simple method of calculating Kazhdan constants for various compact subsets of semisimple $G$.

Citation

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Hee Oh. "Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants." Duke Math. J. 113 (1) 133 - 192, 15 May 2002. https://doi.org/10.1215/S0012-7094-02-11314-3

Information

Published: 15 May 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1011.22007
MathSciNet: MR1905394
Digital Object Identifier: 10.1215/S0012-7094-02-11314-3

Subjects:
Primary: 22E46
Secondary: 22E50

Rights: Copyright © 2002 Duke University Press

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Vol.113 • No. 1 • 15 May 2002
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