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

Moeglin, Colette

HAL, hal-00003594 / Harvested from HAL

Résumé

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.

Détail

Publié le : 2004-12-15
Classification:  representations,  Arthur's packets,  stability,  p-adic groups,  2.2e+51,  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]