Sur les paquets d'Arthur aux places réelles, 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 $ψ: W_{\mathbb R}\times \mathbf{SL}_2(\mathbb C)\rightarrow {}^LG$ be an Arthur parameter for $G$. Let $A(ψ)$ the component group of the centralizer of $ψ$ in $\hat G$. Attached to $ψ$ is a finite length unitary representation $π^A(ψ)$ of $G\times A(ψ)$, 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 $π^A(ψ)$ when the parameter $ψ$ is "very regular, with good parity". In the present paper, we use translation of infinitesimal character to describe $π^A(ψ)$ in the general good parity case from the representation $π^A(ψ_+)$ attached to a very regular, with good parity, parameter $ψ_+$ obtained from $ψ$ by a simple shift.