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

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 $({\mathrm{Sp}}_{2n},\mathrm{O}(V))$ 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.