Related papers: Theta Correspondence and Arthur packets

In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This…

We establish the invariant trace formula (\`a la Arthur) for the ad\'elic covers of connected reductive groups over a number field, under the hypothesis that the trace Paley-Wiener theorem is verified for all Levi subgroups at the real…

The purpose of this paper is to show that under a part of generalized Arthur's A-packet conjecture, locally generic cuspidal automorphic representations of a quasisplit group over a number field are of Ramanujan type, i.e., are tempered at…

Nous \'etendons aux groupes orthogonaux et unitaires non quasi-d\'eploy\'es sur un corps local des r\'esultats de J. Arthur et de la premi\`ere auteure \'etablis dans le cas quasi-d\'eploy\'e. En particulier, nous obtenons une…

We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about…

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its…

Generalizing the proof -- by Hecht and Schmid -- of Osborne's conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle -- stated…

In this paper, we highlight and state precisely the local Langlands correspondence for quasi-split O_{2n} established by Arthur. We give two applications: Prasad's conjecture and Gross--Prasad conjecture for O_{n}. Also, we discuss the…

In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur…

Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the "Langlands element" (i.e., the one specified by Arthur) of all unipotent…

Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various…

In this paper we compute the multiplicities appearing in the ${\overline{\mathbb{F}}_\ell}$-modular theta correspondence in type II over a non-archimedean field $\mathrm{F}$, where $\ell$ is a prime not dividing the residue cardinality of…

The local intertwining relation is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. We prove several instances of the local intertwining relation for…

Let $G=\mathbf{G}(\mathbb{R})$ be the group of real points of a quasi-split connected reductive algebraic group defined over $\mathbb{R}$. Assume furthermore that $G$ is a classical group (symplectic, special orthogonal or unitary). We show…

In this paper, we completely describe the Howe correspondence for the dual pairs from the title over a nonarchimedean local field of characteristic zero. More specifically, for every irreducible admissible representation of these groups, we…

In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic…

We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong…

This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$. The focus is on complexes that have length $\mathrm{dim}\, R$, which is the smallest possible value, and in particular on…

In this paper, we give an explicit determination of the theta lifting for symplectic-orthogonal and unitary dual pairs over a nonarchimedean field $F$ of characteristic $0$. We determine when theta lifts of tempered representations are…