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 $\psi :W_{\mathbb{R}}\times {\mathbf{SL}}_2(\mathbb{C})\to {}^{L}G$ 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.

arXiv comment22 pages, in French. V2 small mistakes corrected

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