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Abstract
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Nous donnons une construction explicite des paquets d’Arthur des groupes unitaires
réels par induction cohomologique et induction parabolique et en suivant une idée
communiquée par P. Trapa, nous établissons la propriété de multiplicité un de
ceux-ci. Nous montrons en particulier des résultats d’irréductibilité de certaines
induites paraboliques pour les groupes unitaires, ce qui nous permet de compléter
les démonstrations d’énoncés analogues annoncés dans nos travaux sur les
paquets d’Arthur des groupes classiques.
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.
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Keywords
Arthur packets, unitary groups, classical groups
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Mathematical Subject Classification 2010
Primary: 20G05, 22E50
Secondary: 11F55
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Milestones
Received: 14 May 2018
Accepted: 29 September 2018
Published: 18 April 2019
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