English

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

Group Theory 2007-05-23 v1

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 GG over a p-adic field FF. An Arthur's packet correspond to a map ψ\psi from WF×SL(2,C)×SL(2,C)W_{F} \times SL(2,{\mathbb C}) \times SL(2,{\mathbb C}) into the LL-group of GG. The packets we consider here have the property that the centralizer of ψ\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 ψ\psi and a character of the centralizer of ψ\psi in the L-group in the Grothendieck group. Stability properties follow easily from analogous properties for the tempered packet which enter the situation.

Keywords

Cite

@article{arxiv.math/0412315,
  title  = {Paquets d'Arthur discrets pour un groupe classique p-adique},
  author = {Colette Moeglin},
  journal= {arXiv preprint arXiv:math/0412315},
  year   = {2007}
}

Comments

Octobre 2004