Related papers: Generic cuspidal representations of $U(2,1)$

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…

We describe a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. Roughly speaking, we require the…

Fix $n \geq 2$ an integer, and let $F$ be a totally real number field. We derive estimates for the finite parts of the $L$-functions of irreducible cuspidal $\operatorname{GL}_n({\bf{A}}_F)$-automorphic representations twisted by class…

In this paper, we begin the study of poles of partial L-functions L^S(sigma tensor tau,s), where sigma tensor tau is an irreducible, automorphic, cuspidal, generic (i.e. with nontrivial Whittaker coefficient) representation of G_A x…

We introduce a categorical framework for the study of representations of $G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that the space 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 $G$ be a classical group over a non-Archimedean local field of odd residual characteristic. Using recent work of S. Stevens, we define a certain kind of semisimple stratum, called good, and show that it provides a simple type in $G$…

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

Let H be a connected reductive group defined over a non-archimedean local field F of characteristic p>0. Using Poincar\'e series, we globalize supercuspidal representations of H(F) in such a way that we have control over ramification at all…

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. To any irreducible smooth…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

Given a (complex, smooth) irreducible representation $\pi$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $\sigma$ of a classical group, we show that the (normalized) parabolic…

We show that an irreducible cuspidal automorphic representation of the group GSp(4,A), which is not CAP and whose infinite component belongs to the discrete series, is weakly equivalent to an irreducible generic automorphic cuspidal…

In the case of p-adic general linear groups, each irreducible representation is parabolically induced by a tensor product of irreducible representations supported by cuspidal lines. One gets in this way a parameterization of the irreducible…

We give the decomposition into irreducible representations of the restriction to a maximal compact subgroup of any irreducible depth-zero supercuspidal representation of $\mathrm{SL}(2,F)$ when $F$ is a local nonarchimedean field of…

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…

For reductive groups $G$ over a number field we discuss automorphic liftings from cuspidal irreducible automorphic representations $\pi$ of $G(\mathbb{A})$ to cuspidal irreducible automorphic representations on $H(\mathbb{A})$ for the…

Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive integer. A smooth irreducible representation of the group $GL(n,K)$ is said to be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant linear form.…

Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $\theta$. Under the assumption that there exists a maximally $\theta$-split torus in $\mathbb{G}$, which…