Related papers: Klyachko models for ladder representations

We study Klyachko models of ${\rm SL}(n, F)$, where $F$ is a nonarchimedean local field. In particular, using results of Klyachko models for ${\rm GL}(n, F)$ due to Heumos, Rallis, Offen and Sayag, we give statements of existence,…

We show that every irreducible representation in the discrete automorphic spectrum of GL(n) admits a non vanishing mixed (Whittaker-symplectic) period integral. The analog local problem is a study of models first considered by Klyachko over…

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…

In this article we explore the interplay between two generalizations of the Whittaker model, namely the Klyachko models and the degenerate Whittaker models, and two functorial constructions, namely base change and automorphic induction, for…

Let $\mathrm{F}$ be a local non-archimedean field of residue characteristic $p$ and $\overline{\mathbb{F}}_\ell$ an algebraic closure of a finite field of characteristic $\ell \neq p$. We extend the results of Lapid and M\'inguez concerning…

Let $D$ denote a quaternion division algebra over a non-archimedean local field $F$ with characteristic zero. Let $Sp_n(D)$ be the unique non-split inner form of the symplectic group $Sp_{2n}(F)$. An irreducible admissible representation…

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.

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. We classify all smooth…

Let E/F be a quadratic extension of non-archimedean local fields of characteristic 0. In this paper, we investigate two approaches which attempt to describe the smooth irreducible representations of GL(n,E) that are distinguished by its…

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…

The SL(2)-type of any smooth, irreducible and unitarizable representation of GL(n) over a p-adic field was defined by Venkatesh. We provide a natural way to extend the definition to all smooth and irreducible representations. For…

In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which…

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of…

Let $E/F$ be a finite cyclic extension of local fields of characteristic zero, of degree $d$, and $\kappa$ be a character of $F^\times$ whose kernel is $\mathrm{N}_{E/F}(E^\times)$. For $m\in \mathbb{N}^*$, we prove that every irreducible…

In 1980 Zelevinsky introduced commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate…

Behind this sophisticated title hides an elementary exercise on Clifford theory for index two subgroups and self-dual/conjugate-dual representations. When applied to semi-simple representations of the Weil-Deligne group $W'_F$ of a non…

Let $F$ be a non-archimedean local field. The classification of the irreducible representations of $GL_n(F)$, $n\ge0$ in terms of supercuspidal representations is one of the highlights of the Bernstein--Zelevinsky theory. We give an…

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…

In this paper, we recover certain known results about the ladder representations of GL(n, Q_p) defined and studied by Lapid, Minguez, and Tadic. We work in the equivalent setting of graded Hecke algebra modules. Using the Arakawa-Suzuki…

Let $G_n$ denote either the group $Sp(2n, F)$ or $SO(2n+1, F)$ over a non-archimedean local field $F$. We determine the composition series of representations of $G_n$ induced from cuspidal and ladder representations such that the minimal…