Theta Lifts of Tempered Representations for Dual Pairs (Sp2n, O(V))

This paper is the continuation of our previous work on the explicit determination of the structure of theta lifts for dual pairs (Sp(2n), O(V)) over a non-archimedean field F of characteristic different than 2, where n is the split rank Of Sp(2n) and the dimension of the space V (over F) is even. We determine the structure of theta lifts of tempered representations in terms of theta lifts of representations in discrete series.