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.

MSC Classifications:

22E35, 22E50, 11F70 show english descriptions Analysis on $p$-adic Lie groups
Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Representation-theoretic methods; automorphic representations over local and global fields 22E35 - Analysis on $p$-adic Lie groups
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
11F70 - Representation-theoretic methods; automorphic representations over local and global fields

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