Related papers: Distinction inside L-packets of SL(n)

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

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 $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…

Let $E/F$ be a quadratic extension of fields, and $G$ a connected quasi-split reductive group over $F$. Let $G^{op}$ be the opposition group obtained by twisting $G$ by the duality involution considered by Prasad. Assume that the field $F$…

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…

Let F be a non-Archimedean locally compact field of residue characteristic p, let G be an inner form of GL(n,F) with n>0, and let l be a prime number different from p. We describe the block decomposition of the category of finite length…

Let $E$ be a non-Archimedian local field of characteristic zero and residue characteristic $p$. Let ${\bf G}$ be a connected reductive group defined over $E$ and $\pi$ an irreducible admissible representation of $G={\bf G}(E)$. A result of…

Let $G$ be a connected reductive group over a field $F=\mathbb{F}_q((t))$ splitting over $\overline{\mathbb{F}}_q((t))$. Following [KV,DR], a tamely unramified Langlands parameter $\lambda:W_F\to{}^L G(\overline{\mathbb{Q}}_{\ell})$ in…

As a consequence of his numerical local Langlands correspondence for $GL(n)$, Henniart deduced the following theorem: If $F$ is a nonarchimedean local field and if $\pi$ is an irreducible admissible representation of $GL(n,F)$, then, after…

Let $G$ be a classical group defined over a local field $F$ of characteristic zero. For any irreducible admissible representation $\pi$ of $G(F)$, which is of Casselman-Wallach type if $F$ is archimedean, we extend the study of spectral…

We study representations of $GL_{n}(\mathbb{F}_{q})$ that are distinguished with respect to a symmetric subgroup $H=GL_{n}(\mathbb{F}_{q})^{\sigma}$, where $\sigma$ is an involution. We prove that those representations satisfy $\pi \cong…

Let $p$ and $l$ be distinct odd primes and let $n\geq 2$ be a positive integer. Let $E$ be a finite Galois extension of degree $l$ of a $p$-adic field $F$. Let $q$ be the cardinality of the residue field of $F$. Let $\overline{\pi}_F$ be a…

Given a quasi-split connected reductive $\mathbb{R}$-group $G$ and a finite group $A$ acting on $G$ by $\mathbb{R}$-automorphisms that preserve an $\mathbb{R}$-pinning, we construct for each discrete $L$-parameter for $G$ a corresponding…

Let F be a non-archimedean local field, of characteristic 0. Let V be a finite dimensional vector space over F and q be a non-degenerate quadratic form on V. Denote d the dimension of V and G=SO(d) the special orthogonal group of (V,q). Let…

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…

Let $E/F$ be a quadratic unramified extension of non-archimedean local fields and $\mathbb H$ a simply connected semisimple algebraic group defined and split over $F$. We establish general results (multiplicities, test vectors) on $\HH…

Let $\mathfrak{o}_l$ be a finite principal ideal local ring of length $l$. The degenerate Whittaker space associated with a representation of ${\rm GL}_{2n}(\mathfrak{o}_l)$ is a representation of ${\rm GL}_n(\mathfrak{o}_l)$. For strongly…

Let $E/F$ be a quadratic extension of a non-Archimedian local field. Splitting of the 2-fold metaplectic cover of ${\rm Sp}_{2n}(F)$ when restricted to various subgroups of ${\rm Sp}_{2n}(F)$ plays an important role in application of the…

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 $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let…