We give a new proof of the existence of Klyachko models for unitary representations of @math over a non-archimedean local field @math . Our methods are purely local and are based on studying distinction within the class of ladder representations introduced by Lapid and Minguez. We classify those ladder representations that are distinguished with respect to Klyachko models. We prove the hereditary property of these models for induced representations from arbitrary finite length representations. Finally, in the other direction and in the context of admissible representations induced from ladder, we study the relation between distinction of the parabolic induction with respect to the symplectic groups and distinction of the inducing data.
Let E F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on ( GL _ n ( A _ E ) ) over a unitary group of a Hermitian form with respect to E F. We provide factorization for these periods into locally defined functionals, express these factors in terms of suitably defined local periods and characterize global distinction. We also study in detail the analogous local question and analyze the space of invariant linear forms under a unitary group. Let E F be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group (GL_n(E) ) which is contragredient to its own Galois conjugate, possesses the expected distinction properties relative to the subgroup (GL_n(F) ). This affirms a conjecture attributed to Jacquet for a large class of representations. Along the way, we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations.