engleski

On the structure of theta lifts of discrete series for dual pairs (Sp(n), O(V))

The purpose of the present paper is to prove some fundamental results on the structure of theta lifts of discrete series. The author shows that the lifts of discrete series behave very much like the lifts of supercuspidal representations. Some of that is already well-known by the previous work of the author, and it is just a corollary of more general and more precise results obtained in this paper. The proof in earlier paper rely on the classification of discrete series for classical groups due to Moeglin and Tadic. The classification of Moeglin and Tadic, is based on an assumption that is not verified yet to its full extent. Therefore, the author does not use their classification, but some very simple properties of discrete series that are verified in the present paper.

non-archimedean fields; symplectic groups; orhogonal groups; discrete series; theta lifts

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