Geometric Weil representation: local field case

Let k be an algebraically closed field of characteristic >2, F=k((t)) and Mp(F) denote the metaplectic extension of Sp_{2d}(F). In this paper we propose a geometric analog of the Weil representation of Mp(F). This is a category of certain perverse sheaves on some stack, on which Mp(F) acts by functors. This construction will be used in math.RT/0701170 (and subsequent publications) for a proof of the geometric Langlands functoriality for some dual reductive pairs.Comment: LaTeX2e, 37 page

Paquets d'Arthur discrets pour un groupe classique p-adique

In this paper we construct some packets of representations which have to correspond to relatively general Arthurs packets; this is for any classical group $G$ over a p-adic field $F$. An Arthur's packet correspond to a map $\psi$ from $W_{F} \times SL(2,{\mathbb C}) \times SL(2,{\mathbb C})$ into the $L$-group of $G$. The packets we consider here have the property that the centralizer of $\psi$ in the dual group is a finite groupe. Our construction is a combinatorial one which reduce the study of the representations in such a packet to tempered representation of eventualy smaller groups; in fact we give a precise description of the representations associated to $\psi$ and a character of the centralizer of $\psi$ in the L-group in the Grothendieck group. Stability properties follow easily from analogous properties for the tempered packet which enter the situation.Comment: Octobre 200

Classification des s\'{e}ries discr\`{e}tes pour certains groupes classiques p-adiques

The goal of this paper is to prove how Arthur's results, in the case of split odd orthogonal p-adic groups, imply the Langlands' classification of discrete series. Of course this need the validity of ''fundamental'' lemmas which are not yet available. And this include a Langlands' classification of cuspidal irreducible representations for such groups

Fonctions L de paires pour les groupes classiques

Let $\pi$ be a square integrable representation of a classical group and let $\rho$ be a cuspidal representation of a general linear group. We can define in two different ways an L-function $L(\rho \times \pi,s)$: first we can use the Langlands parametrization at each places which is now available, thanks to Arthur's work, and secondly we can transfer $\pi$ to a general linear group, using the twisted endoscopy as established by Arthur. In this paper, we compare the two definitions and we prove, as expected, that the first one has less poles that the second one. Assuming that $\pi$ is cuspidal, we link the poles of the first L-function to the poles of the Eisensteins series and when $\rho$ is a quadratic character and when the groupe is a special orthogonal group, we also link theses poles with the theta lifts. We have some hypothesis at the archimedean places

Classification et changement de bases pour les séries discrètes des groupes unitaires p-adiques.

This paper deals with the Langlands' classification for discrete series of unitary quasi-split p-adic groups. We show that such a classification follows from Arthur's work on the simple trace formula which we can use now thanks to Laumon-Ngo's proof of the fundamental lemma and Waldspurger's work on the consequences of it on the transfer