English

Sur les paquets d'Arthur aux places r\'eelles, translation

Representation Theory 2017-07-19 v2

Abstract

This article is part of a project which aims to describe as explicitly as possible the Arthur packets of classical real groups and to prove a multiplicity one result for them. Let GG be a symplectic or special orthogonal real group, and ψ:WR×SL2(C)LG\psi: W_{\mathbb R}\times \mathbf{SL}_2(\mathbb C)\rightarrow {}^LG be an Arthur parameter for GG. Let A(ψ)A(\psi) the component group of the centralizer of ψ\psi in G^\hat G. Attached to ψ\psi is a finite length unitary representation πA(ψ)\pi^A(\psi) of G×A(ψ)G\times A(\psi), which is characterized by the endoscopic identities (ordinary and twisted) it satisfies. In [arXiv:1703.07226] we gave a description of the irreducible components of πA(ψ)\pi^A(\psi) when the parameter ψ\psi is "very regular, with good parity". In the present paper, we use translation of infinitesimal character to describe πA(ψ)\pi^A(\psi) in the general good parity case from the representation πA(ψ+)\pi^A(\psi_+) attached to a very regular, with good parity, parameter ψ+\psi_+ obtained from ψ\psi by a simple shift.

Keywords

Cite

@article{arxiv.1704.05096,
  title  = {Sur les paquets d'Arthur aux places r\'eelles, translation},
  author = {Colette Moeglin and David Renard},
  journal= {arXiv preprint arXiv:1704.05096},
  year   = {2017}
}

Comments

22 pages, in French. V2 small mistakes corrected