Comparaisons des exposants \`a l'int\'erieur d'un paquet d'Arthur archim\'edien

TL;DR

This paper generalizes a proof of Osborne's conjecture to establish an Archimedean version of a theorem by Moeglin, clarifying the structure of local Arthur packets and their relation to local L-packets and tempered representations.

Contribution

It provides a precise Archimedean version of the principle linking Arthur packets, L-packets, and tempered representations, extending previous results to a broader context.

Findings

Proved an Archimedean version of Moeglin's theorem

Established that local Arthur packets contain the corresponding local L-packets

Showed that these packets include more tempered representations

Abstract

Generalizing the proof -- by Hecht and Schmid -- of Osborne's conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle -- stated by the second author -- according to which {\it a local Arthur packet contains the corresponding local $L$-packet and representations which are more tempered.}