Filtration de certains espaces de fonctions sur un espace symétrique réductif

We introduce a filtration of a ( g,K) -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.