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Comptes Rendus Mathématique
Volume 343, n° 3
pages 165-168 (août 2006)
Doi : 10.1016/j.crma.2006.06.012
Received : 6 May 2006 ;  accepted : 6 June 2006
A refinement of Harish-Chandraʼs method of descent
Une extension de la méthode de descente de Harish-Chandra
 

Florent Bernon
Département de mathématiques, université Paris X-Nanterre, 200, avenue de la République, 92000 Nanterre, France 

Abstract

Let G be a connected real reductive group and M a connected reductive subgroup of G with Lie algebras   and   respectively. We assume that   and   have the same rank. We define a map from the space of orbital integrals of   into the space of orbital integrals of   which we call a transfer. The transpose of the transfer can be viewed as a map from the space of G-invariant distributions of   to the space of M-invariant distributions of   and can be considered as a restriction map from   to  . We prove that this restriction map extends Harish Chandraʼs method of descent and we obtain a generalization of Harish-Chandraʼs radial component theorem. To cite this article: F. Bernon, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Résumé

Soient G un groupe réductif réel connexe et M un sous-groupe réductif connexe de G dʼalgèbres de Lie respectivement   et  . On suppose que   et   ont le même rang. Nous prouvons quʼil existe une application de lʼespace des intégrales orbitales de   dans lʼespace des intégrales orbitales de   que lʼon appelle un transfert. La transposée de ce transfert définit une application de lʼespace des distributions G-invariante sur   dans lʼespace des distributions M-invariantes sur   et peut être considérée comme une restriction. On montre que cette application de restriction étend la méthode de descente de Harish-Chandra et on obtient une généralisation du théorème de la composante radiale de Harish-Chandra. Pour citer cet article : F. Bernon, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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


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