Paquets d'Arthur des groupes classiques complexes

TL;DR

This paper explicitly describes Arthur packets for complex classical groups and their internal parametrization, showing their construction via parabolic induction from unipotent packets and their coincidence with Barbasch-Vogan packets.

Contribution

It provides an explicit parametrization of Arthur packets for complex classical groups and links them to unipotent packets and Barbasch-Vogan constructions.

Findings

Arthur packets are obtained by parabolic induction from unipotent packets.

Unipotent packets of good parity coincide with Barbasch-Vogan packets.

Deep results of Barbasch are used to classify the unitary dual of these groups.

Abstract

Nous d\'ecrivons explicitement les paquets d'Arthur des groupes classiques complexes, ainsi que leur param\'etrisation interne par les caract\`eres du groupe des composantes connexes du centralisateur de leur param\`etre. Nous montrons d'abord qu'ils sont obtenus par induction parabolique pr\'eservant l'irr\'eductibilit\'e \`a partir des paquets unipotents de "bonne parit\'e". Pour ceux-ci, nous montrons qu'ils co\"incident avec les paquets d\'efinis par Barbasch-Vogan. Nous utilisons des r\'esultats profonds de Barbasch entrant dans sa classification du dual unitaire de ces groupes. We describe explicitly Arthur packets for complex classical groups, as well as their internal parametrization by the group of characters of the component group of the stabilizer of their parameter. We first show that they are obtained by parabolic induction preserving irreducibility from unipotent packets of "good parity". For these, we show that they coincide with the packets defined by Barbasch and Vogan. We use deep results of Barbasch entering his classification of the unitary dual of these groups.