Abstract 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.