Theta lifts of generic representations for dual pairs $$(\text {Sp}_{2n}, \text {O}(V))$$

Abstract

We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups $$(\text {Sp}_{2n}, \text {O}(V))$$ defined over a local nonarchimedean field $${\mathbb {F}}$$ of characteristic 0. As a direct application of our results, we are able to produce a series of non-generic unitarizable representations of these groups.