Filtration de certains espaces de fonctions sur un espace symétrique réductif |
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| Authors: | P Delorme |
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| Institution: | a Institut de Mathématiques de Luminy, UPR 9016 du C.N.R.S, Université de la Méditerranée, 163, avenue de Luminy - Case 907, 13288 Marseille Cedex 9, France
b IRMA-UFR de Mathématique et d'Informatique de Strasbourg, 7, rue René Descartes, 67084 Strasbourg Cedex, France |
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| Abstract: | We introduce a filtration of a  -module of some space of functions on a reductive symmetric space G/H, and compute the associated grading as a direct sum of induced representations. As an application of this result to the reductive groups viewed as symmetric spaces, we are able to realize any Harish-Chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups, the inducing representations being trivial on the unipotent radical. |
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| Keywords: | Reductive symmetric spaces Invariant differential operators Eigenfunctions Generalized principal series Harish-Chandra modules Sub-quotient theorem |
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