THETA LIFTS OF STRONGLY POSITIVE DISCRETE SERIES: THE CASE OF(Sp(n), O(V))

摘要

Let F denote a nonarchimedean local field of characteristic zero with odd residual characteristic. Using the results of Gan and Savin, in this paper we determine the first occurrence indices and theta lifts of strongly positive discrete series representations of metaplectic groups over F in terms of our recent classification of this class of representations. Also, we determine the first occurrence indices of some strongly positive representations of odd orthogonal groups.