Related papers: Archimedean Distinguished Representations and Exce…

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 $\F$ 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…

We will give an explicit construction of irreducible suparcuspidal representations of the special linear group over a non-archimedean local field and will speculate its Langlands parameter by means of verifying the Hiraga-Ichino-Ikeda…

Let $F$ be a locally compact non-Archimedean field, and $\bf G$ a connected quasi-split reductive group over $F$. We are interested in complex irreducible smooth generic representations $\pi$ of ${\bf G}(F)$. When $F$ has positive…

Let F be a p-adic field and let G(n) and G`(n) be the metaplectic double covers of the general symplectic group and symplectic group attached to a 2n dimensional symplectic space over F. We show here that if n is odd then all the genuine…

Let $F$ be a finite extension of $\mathbb{Q}_p$ and let $E$ be a quadratic extension of $F$. A representation $(\pi,V)$ of ${\rm GL}_n(E)$ is said to be ${\rm GL}_n(F)$-distinguished if there exists a non-zero linear functional $\phi$ on…

Let $p>3$ be a prime, $n>1$ be an integer, and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. Let $E$ be an algebraically closed countable field extension of the residue field of $F$. In…

We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman-Wallach representation of $\mathrm{GL}_n$ that quantifies the extent to which this representation may be ramified. We also determine a distinguished…

For the discrete series representations of ${\rm GL}(n)$ over a non-archimedean local field $F$, we define a notion of functions similar to "zonal spherical functions" for unramified principal series. We prove the existence of such…

Let $\rho$ is a cuspidal representation of $GL(n,F)$, with $F$ a non archimedean local field, and $H$ a maximal Levi subgroup of $GL(n,F)$. We show that if $\rho$ is $H$-distinguished, then $n$ is even, and $H\simeq GL(n/2,F)\times…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic 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…

Let $F$ be a non-Archimedean local field and let $p$ be the residual characteristic of $F$. Let $G=GL_2(F)$ and let $P$ be a Borel subgroup of $G$. In this paper we study the restriction of irreducible representations of $G$ on $E$-vector…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

Let $F$ be a $p$-adic field and choose $k$ an algebraic closure of $\mathbb{F}_{\ell}$, with $\ell$ different from $p$. We define ``nilpotent lifts'' of irreducible generic $k$-representations of $GL_n(F)$, which take coefficients in Artin…

Let $F$ be a finite field, and let $\mathbb{E}$ be either a quadratic field extension $E/F$ or the split algebra $F \oplus F$. We study distinguished representations of $\rm{SL}_{2n}(F)$ by the subgroup $H_{\flat} := \rm{SL}_{2n}(F) \cap…

We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive $p$-adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We…

Let $F$ be a finite extension of ${\mathbb{Q}} \_p$. Any dihedral supercuspidal representation of $GL \_2 (K)$ arises from an admissible multiplicative character $\omega$ of a quadratic extension $L$ of $K$. We show that such a…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$, and let $\sigma$ denote its non-trivial automorphism. Let $R$ be an algebraically closed field of characteristic different…