Uniqueness and disjointness of Klyachko models

We show the uniqueness and disjointness of Klyachko models for GL(n,F) over a non-archimedean local field F. This completes, in particular, the study of Klyachko models on the unitary dual. Our local results imply a global rigidity property for the discrete automorphic spectrum

On Unitary Representations of GL2n Distinguished by the Symplectic Group

We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a result of M. Heumos and S. Rallis our methods, unlike their purely local technique, re- lies on the theory of automorphic forms. The results of this paper together with later works by the authors imply that the family of representations studied in this paper contains all irreducible, unitary representations of the general linear group that are distin- guished by the symplectic group.Comment: Two references added and minor editing of the published versio

On local intertwining periods

We prove the absolute convergence, functional equations and meromorphic continuation of local intertwining periods on parabolically induced representations of finite length for certain symmetric spaces over local fields of characteristic zero, including Galois pairs as well as pairs of Prasad and Takloo-Bighash type. Furthermore, for a general symmetric space we prove a sufficient condition for distinction of an induced representation in terms of distinction of its inducing data. Both results generalize previous results of the first two named authors. In particular, for both we remove a boundedness assumption on the inducing data and for the second we further remove any assumption on the symmetric space. Moreover, when the inducing representation is uniformly bounded, we extend the field of cofficients from p-adic to any local field of characteristic zero. In fact this extension holds for all finite length representations under a natural generic irreducibility assumption for parabolic induction. In the case of p-adic symmetric spaces, combined with the necessary conditions for distinction that follow from the geometric lemma, this provides a necessary and sufficient condition for distinction of representations induced from cuspidal.Comment: 28 pages; in this version we extend the field of cofficients from p-adic to any local field of characteristic zer

Existence of Klyachko Models for GL(n;R) and GL(n;C)

We prove that any unitary representation of GL(n;R) and GL(n;C) admits an equivariant linear form with respect to one of the subgroups considered by Klyachko