On irreducible generic representations distinguished by orthogonal groups

Let F be a local non-archimedean field of characteristic zero. We provide a classification of the irreducible, generic representations of GL(n,F) which are distinguished by an orthogonal group modulo the corresponding classification for quasi-square-integrable representations. More precisely, we prove that an irreducible, generic representation of GL(n,F) is distinguished by an orthogonal group if and only if the corresponding inducing quasi-square integrable representations are distinguished by appropriate orthogonal groups.