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15 February 2005 ν-tempered representations of p-adic groups, I: l-adic case
J.-F. Dat
Duke Math. J. 126(3): 397-469 (15 February 2005). DOI: 10.1215/S0012-7094-04-12631-4


The so-called tempered complex smooth representations of p-adic groups have been much studied and used, in connection with automorphic forms. Nevertheless, the smooth representations that are realized geometrically often have l-adic coefficients, so that Archimedean estimates of their matrix coefficients hardly make sense. We investigate here a notion of tempered representation with coefficients in any normed field of characteristic not equal to p. The theory turns out to be different according to the norm being Archimedean, non-Archimedean with |p| ≠ 1, or non-Archimedean with |p|= 1.

In this paper we concentrate on the last case. The main applications concern modular representation theory (i.e., on a positive characteristic field) and, in particular, the study of reducibility properties of the parabolic induction functors; one of the main results is the generic irreducibility for induced families. Thanks to a suitable theory of rational intertwining operators, this allows us to define Harish-Chandra's μ-functions and show in some special cases how they track down the cuspidal constituents of parabolically induced representations. Besides, we discuss the admissibility of parabolic restriction functors and derive some lifting properties for supercuspidal modular representations.


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J.-F. Dat. "ν-tempered representations of p-adic groups, I: l-adic case." Duke Math. J. 126 (3) 397 - 469, 15 February 2005.


Published: 15 February 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1063.22017
MathSciNet: MR2120114
Digital Object Identifier: 10.1215/S0012-7094-04-12631-4

Primary: 22E50
Secondary: 11F70 , 20G05

Rights: Copyright © 2005 Duke University Press


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Vol.126 • No. 3 • 15 February 2005
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