Journal of Lie Theory, 7(2), 201-229 (1997)
Non nullité de certains relêvements par séries théta
Université Paris 7
F-75251 Paris cedex 05
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.
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