The local theta correspondence for unramified unitary groups (Q1905795)

Let \(F\) be a non-archimedean local field. The author considers the dual reductive pair \((U_{2n}, U_{2n+1})\) over \(F\) where \(U_{2n}\) and \(U_{2n+1}\) are quasisplit unitary groups over \(F\). The purpose of this paper is to determine the image of the theta correspondence from \(U_{2n}\) to \(U_{2n+1}\) and from \(U_{2n+1}\) to \(U_{2n+2}\). The author computes the correspondence explicitly for spherical representations in these two cases.