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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1189-1195 (octobre 2009)
Doi : 10.1016/j.crma.2009.09.014
Received : 23 July 2009 ;  accepted : 2 September 2009
Laplacien hypoelliptique et intégrales orbitales
Hypoelliptic Laplacian and orbital integrals
 

Jean-Michel Bismut 1
Département de mathématique, université Paris-Sud, bâtiment 425, 91405 Orsay cedex, France 

Résumé

On donne une nouvelle méthode de calcul d’intégrales orbitales utilisant le Laplacien hypoelliptique. On obtient un formalisme unifiant le théorème de l’indice d’Atiyah–Singer et la formule des traces. Pour citer cet article : J.-M. Bismut, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
Abstract

We give a new approach to orbital integrals based on the hypoelliptic Laplacian. The formalism unifies the Atiyah–Singer index theorem and the trace formula. To cite this article: J.-M. Bismut, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
1  L’auteur remercie L. Clozel, F. Labourie, W. Müller et Y. Tschinkel pour d’utiles conversations. Il est particulièrement redevable à G. Lebeau pour son aide amicale.


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