Equivalent definitions of Arthur packets for real unitary groups

Abstract

Mok and Moeglin-Renard have defined Arthur packets for unitary groups. Their definitions follow Arthur's work on classical groups and rely on harmonic analysis. For real groups there is an alternative definition of Arthur packets due to Adams-Barbasch-Vogan. It relies on sheaf-theoretic techniques instead of harmonic analysis. We prove that these two definitions of Arthur packets are equivalent in the case of real unitary groups.