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

Abstract

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 $ψ$ 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 $ψ$ 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 $ψ$ and a character of the centralizer of $ψ$ in the L-group in the Grothendieck group. Stability properties follow easily from analogous properties for the tempered packet which enter the situation.