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Israel Journal of Mathematics

, Volume 192, Issue 1, pp 83–120 | Cite as

Automorphic Plancherel density theorem

  • Sug Woo Shin
Article

Abstract

Let F be a totally real field, G a connected reductive group over F, and S a finite set of finite places of F. Assume that G(F ℝ) has a discrete series representation. Building upon work of Sauvageot, Serre, Conrey-Duke-Farmer and others, we prove that the S-components of cuspidal automorphic representations of \(G\left( {\mathbb{A}_F } \right)\) are equidistributed with respect to the Plancherel measure on the unitary dual of G(F S ) in an appropriate sense. A few applications are given, such as the limit multiplicity formula for local representations in the global cuspidal spectrum and a quite flexible existence theorem for cuspidal automorphic representations with prescribed local properties. When F is not a totally real field or G(F ℝ) has no discrete series, we present a weaker version of the above results.

Keywords

Haar Measure Trace Formula Discrete Series Levi Subgroup Automorphic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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