On unitary representations of GL_{2 n} distinguished by the symplectic group

We provide a family of representations of GL_n over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp (n)-distinguished). This is a generalization of a result of Heumos-Rallis. Our proof uses global methods. The results of [Omer Offen, Eitan Sayag, Global mixed periods and local Klyachko models for the general linear group, submitted for publication] imply that the family at hand contains all irreducible, unitary representations that are distinguished by the symplectic group.