Sur les paquets d'Arthur des groupes unitaires et quelques cons\'equences pour les groupes classiques

TL;DR

This paper explicitly constructs Arthur packets for real unitary groups using cohomological and parabolic induction, proving their multiplicity one property and establishing irreducibility of certain induced representations, with implications for classical groups.

Contribution

It provides an explicit construction of Arthur packets for real unitary groups and proves their multiplicity one property, extending results to classical groups.

Findings

Construction of Arthur packets for real unitary groups

Proof of multiplicity one property for these packets

Irreducibility results for certain parabolically induced representations

Abstract

We give an explicit construction of Arthur packets for real unitary groups by cohomological and parabolic induction and following an idea communicated to us by P. Trapa, we show that they satisfy the multiplicity one property. In particular, we show the irreducibility of some parabolically induced representations for unitary groups, and use this to give the proof of analogous statements made in our work on Arthur packets of classical groups. Nous donnons une construction explicite des paquets d'Arthur des groupes unitaires r\'eels par induction cohomologique et induction parabolique et en suivant une id\'ee communiqu\'ee par P. Trapa, nous \'etablissons la propri\'et\'e de multiplicit\'e un de ceux-ci. Nous montrons en particulier des r\'esultats d'irr\'eductibilit\'e de certaines induites paraboliques pour les groupes unitaires, ce qui nous permet de compl\'eter les d\'emonstrations d'\'enonc\'es analogues annonc\'es dans nos travaux sur les paquets d'Arthur des groupes classiques.