Equivalent definitions of Arthur packets for real unitary groups

TL;DR

This paper proves the equivalence of two different definitions of Arthur packets for real unitary groups, one based on harmonic analysis and the other on sheaf-theoretic techniques.

Contribution

It establishes the equivalence between harmonic analysis-based and sheaf-theoretic definitions of Arthur packets for real unitary groups.

Findings

Proves the equivalence of two definitions of Arthur packets for real unitary groups.

Bridges harmonic analysis and sheaf-theoretic approaches in representation theory.

Enhances understanding of the structure of Arthur packets in real 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.