Journal of Lie Theory, 7(2), 231-238 (1997)
Quelques propriétés de base des séries théta
Université Paris 7
F-75251 Paris cedex 05
Abstract: In this article, one studies the basic properties of the theta correspondance between an even othogonal group and a symplectic group. One proves that the image of a cuspidal irreducible representation of one of theses groups by this correspondance is either 0 or irreducible and that the correspondance is involutive and injective when generalized to the Witt towers. Theses results was allready known when the rank of the groups are very different, thanks to works of Rallis. The method is based on the regularized Siegel-Weil formula of Kudla and Rallis and looks like the work of Rallis.
Full text of the article: