**
Journal of Lie Theory, 7(2), 201-229 (1997)
**

#
Non nullité de certains relêvements par séries théta

##
C. Moeglin

Mathématiques

Université Paris 7

F-75251 Paris cedex 05

email moeglin@math.jussieu.fr

**Abstract:** In this article, one studies the theta correspondance between automorphic representations of an even orthogonal group and a symplectic group. Fix an irreducible cuspidal representation, $\pi$, of the othogonal group. One gives a necessary and sufficient condition in order that there exists an adelic character of the orthogonal group, $\eta$ such that the image of $\pi\otimes \eta$ by the correspondance is non zero. One gives also an answer for the symetric question, $\pi$ is now a representation of the symplectic group; here one allows change of the orthogonal space saving the dimension. The method is based on the works of Kudla, Rallis and Piatetskii-Shapiro.
**Full text of the article:**