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

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 $G$ be a symplectic or special orthogonal real group, and $\psi: W_{\mathbb R}\times \mathbf{SL}_2(\mathbb C)\rightarrow {}^LG$ be an Arthur parameter for $G$. Let $A(\psi)$ the component group of the centralizer of $\psi$ in $\hat G$. Attached to $\psi$ is a finite length unitary representation $\pi^A(\psi)$ of $G\times A(\psi)$, 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 $\pi^A(\psi)$ when the parameter $\psi$ is "very regular, with good parity". In the present paper, we use translation of infinitesimal character to describe $\pi^A(\psi)$ in the general good parity case from the representation $\pi^A(\psi_+)$ attached to a very regular, with good parity, parameter $\psi_+$ obtained from $\psi$ by a simple shift.