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Geometric orbital integrals and the center of the enveloping algebra

Published online by Cambridge University Press:  11 August 2022

Jean-Michel Bismut
Institut de Mathématique d'Orsay, Université Paris-Saclay, Bâtiment 307, 91405 Orsay, France
Shu Shen
Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Case Courrier 247, 4 place Jussieu, 75252 Paris Cedex 05, France


The purpose of this paper is to extend the explicit geometric evaluation of semisimple orbital integrals for smooth kernels for the Casimir operator obtained by the first author to the case of kernels for arbitrary elements in the center of the enveloping algebra.

Research Article
© 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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The authors are much indebted to Laurent Clozel for his stimulating remarks during the preparation of the paper, and for reading the preliminary version very carefully. We thank the referee for his helpful remarks.


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