Related papers: The local converse theorem for $Mp_{2n}$ : the gen…

In this article we prove that the gamma factors attached to generic representations of ${\rm U}_{2n+1}\times{\rm Res}_{E/F}{\rm GL}_r$ over a local field $F$ defined by various approaches coincide when $F$ is non-archimedean and under…

Let $F$ be a non Archimedean local field, and $G$ be the $F$-points of a connected quasi-split reductive group defined over $F$. In this note we propose a converse theorem statement for generic Langlands parameters of $G$ when the Langlands…

We prove a descent criterion for certain families of smooth representations of GL_n(F) (F a p-adic field) in terms of the gamma factors of pairs constructed in previous work of the second author. We then use this descent criterion, together…

We extend the theory of local constants to l-adic families of representations of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta integrals and gamma factors for representations coming from the conjectural "local…

In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…

Let F be a non-archimedean local field of characteristic zero. In this paper we construct examples of supercuspidal representations showing that the bound $[N/2]$ for the local converse theorem of $GL_N(F)$ is sharp, N general, when the…

Let $F$ be a $p$-adic field and $\pi$ be an irreducible smooth representation of $\textrm{Sp}_{2n}(F)$. In this paper, we show that if $\pi$ and $\pi^\kappa$ are both generic for a common generic character of the maximal unipotent of a…

In this work we prove that the local $\gamma$-factor arising from the doubling integrals for split general spin groups is stable. This deep property of the $\gamma$-factor constitutes an important ingredient in the application of the…

It is shown for all local fields $\mathbb{F}$ which are of characteristic different from $2$ that any distribution on $GL_{n+1}(\mathbb{F})$ which is invariant under conjugation by $GL_n(\mathbb{F})$ is also invariant under transposition.…

Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for $\mathrm{Sym}^{n}$ lifting from $\mathrm{GL}_{2}$ to $\mathrm{GL}_{n+1}$ over any local fields $F$ of characteristic zero with residue…

We give a direct proof of the local converse theorem for quasi-split non-split $\mathrm{SO}_{2l}$ over a local non-Archimedean field of characteristic $p\neq 2$, applying the theory of Howe vectors and partial Bessel functions.

We prove a rank-two potential automorphy theorem for mod $l$ representations satisfying an ordinary condition. Combined with an ordinary automorphy lifting theorem, we prove a rank-two, $p \ne l$ case of local-global compatibility for…

We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth representations of GL(n,F) where F is a finite extension of Q_p and l is different from p. To do so, we also extend the theory of Rankin-Selberg integrals, first…

We construct a theory of local gamma factors for $G_2 \times GL_r$ using a functorial lifting from $G_2$ to $GL_7$. This theory of gamma factors is uniquely characterized by a usual list of properties, showing that it is the only possible…

Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient…

We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the…

In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…

We study the variation of the local Langlands correspondence for ${\rm GL}_{n}$ in characteristic-zero families. We establish an existence and uniqueness theorem for a correspondence in families, as well as a recognition theorem for when a…

We prove the existence of local constancy phenomena for reductions in a general prime power setting of two-dimensional irreducible crystalline representations. Up to twist, these representations depend on two parameters: a trace $a_p$ and a…

We present an approximate converse theorem which measures how close a given set of irreducible admissible unramified unitary generic local representations of GL(n) is to a genuine cuspidal representation. To get a formula for the measure,…