Related papers: Linear periods for unitary representations

The main aim of this paper is to classify the irreducible admissible representations of ${\rm GL}_{4}(F)$ and ${\rm GL}_{6}(F)$ for a nonarchimedean local field $F$, which bear a nontrivial linear form invariant under the groups ${\rm…

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily…

We study GL_2(F)-invariant periods on representations of GL_2(A), where F is a nonarchimedean local field and A/F a product of field extensions of total degree 3. For irreducible representations, a theorem of Prasad shows that the space of…

Let $F$ be a $p$-adic field ($p\neq 2$), let $E$ be a quadratic Galois extension of $F$, and let $n \geq 2$. We construct representations in the discrete spectrum of the $p$-adic symmetric space $H \backslash G$, where $G =…

Let $F$ be a nonarchimedean local field of characteristic zero and odd residual characteristic. Let $X$ be the $p$-adic symmetric space $X = H \backslash G$, where $G = \mathbf{GL}_{2n}(F)$ and $H = \mathbf{GL}_n(F) \times…

Let $D$ be a quaternion division algebra over a non-archimedean local field $K$ of characteristic zero, and let $Sp_n(D)$ be the unique non-split inner form of the symplectic group $Sp_{2n}(K)$. This paper classifies the irreducible…

In analogy with the study of representations of $GL_{2n}(F)$ distinguished by $Sp_{2n}(F)$, where $F$ is a local field, in this paper we study representations of $U_{2n}(F)$ distinguished by $Sp_{2n}(F)$. (Only quasi-split unitary groups…

Suppose that $F$ is a non-Archimedean local field and $D$ is a central division algebra over $F$. Let $n$ be a positive integer. We show a classification modulo essentially square-integrable representations of standard modules of…

Let $\F$ be a non-Archimedean locally compact field, $q$ be the cardinality of its residue field, and $\R$ be an algebraically closed field of characteristic $\ell$ not dividing $q$.We classify all irredu\-cible smooth $\R$-representations…

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let $\mathbf{Sp}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\geq 2$. We prove that the Speh representations $\mathcal{U}(\delta,2)$,…

Let $F$ be a $p$-adic field. In this article, we consider representations of split special orthogonal groups $\mathrm{SO}_{2n+1}(F)$ and symplectic groups $\mathrm{Sp}_{2n}(F)$ of rank $n$. We denote by $\pi_1 \times \ldots \times \pi_r…

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…

This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for each such…

Let $F$ be a non-archimedean local field with odd residual characteristic, and let $H$ be a maximal torus of ${\rm GL}_2(F)$. In this paper, we will classify the irreducible $H$-distinguished representations of ${\rm GL}_2(F)$ by using…

Let $F$ be an archimedean local field and let $E$ be $F\times F$ (resp. a quadratic extension of $F$). We prove that an irreducible generic (resp. nearly tempered) representation of $\operatorname{GL}_n(E)$ is $\operatorname{GL}_n(F)$…

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…

Let F be a non-Archimedean local field of characteristic 0, and let D be a finite dimensional central division algebra over F. We prove that any unitary irreducible representation of a Levi subgroup of GL(m,D), with m a positive integer,…

Following the regularization method presented by Zydor, we study in this paper the regularized linear periods of square-integrable automormphic forms on $\mathrm{GL}_{2n}(\mathbb{A}_F)$, where $F$ is a number field and $\mathbb{A}_F$ its…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields with residual characteristic $p\neq2$, and $\ell$ be a prime number different from $p$. We classify those $\ell$-modular cuspidal irreducible representations of…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the unramified unitary group U(2,2) defined over F_0. In this paper, we give a classification of the irreducible smooth representations of G of…