Related papers: Typical representations for level zero Bernstein c…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$ with Galois automorphism $\sigma$, and let $R$ be an algebraically closed field of characteristic $\ell\notin\{0,p\}$. We…

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…

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the…

Let F be a finite extension of Q_p and let G be a connected reductive group over F. We assume that p is big relatively to G. Let G' be an endoscopic group of G. Following Arthur, we have, roughly speaking, a spectral transfer which, to a…

We will construct a family of irreducible generic supercuspidal representations of the symplectic groups over non-archimedian local field $F$ of odd residual characteristic. The supercuspidal representations are compactly induced from…

We give a description of all the cuspidal representations of $\mathrm{GL}_4(\mathfrak{o}_2)$, where $\mathfrak{o}_2$ is a finite ring coming from the ring of integers in a local field, modulo the square of its maximal ideal $\mathfrak{p}$.…

Let $F$ be a non-Archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $\pi$, there exists a $[G, \pi]_{G}$-type $(J,…

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 $G_n=\operatorname{GL}_n(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$. Our starting point is the Bernstein-decomposition of the representation category of $G_n$ over an algebraically closed field of…

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 $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$. Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal representation, $\bar{\pi}$, of $G$ over a sufficiently large finite field, $k$, of…

Let $\pi$ be a cuspidal automorphic representation of $\mathrm{GSp}_4(\mathbf{A_Q})$, whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If $\pi$ is not CAP or endoscopic, then we show…

Let ${\bf G}$ be a split classical group over a non-Archimedean local field $F$ with the cardinality of the residue field $q_F>5$. Let $M$ be the group of $F$-points of a Levi factor of a proper $F$-parabolic subgroup of ${\bf G}$. Let $[M,…

Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ which satisfies certain reasonable assumptions such as integrality of Hecke polynomials, the existence of mod $\ell$ Galois representations attached to…

In this paper, we compute irreducible components which appear in the stable reduction of the Lubin-Tate curve of level two, in the mixed characteristic case. We also compute the action of the central division algebra of invariant 1/2, the…

Let $k$ be an algebraically closed field of characteristic $l\neq p$. We construct maximal simple cuspidal $k$-types of Levi subgroups $\mathrm{M}'$ of $\mathrm{SL}_n(F)$, when $F$ is a non-archimedean locally compact field of residual…

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation \pi of GSp(4,F), where F is a…

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…

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…