Endoscopic classification of representations of quasi-split unitary groups

TL;DR

This paper establishes the endoscopic classification of tempered and discrete automorphic representations of quasi-split unitary groups over local and global fields, extending Arthur's methods to this class of groups.

Contribution

It provides the first comprehensive endoscopic classification for quasi-split unitary groups, adapting Arthur's trace formula techniques to these groups.

Findings

Classification of tempered representations over local fields

Classification of automorphic spectrum over global fields

Extension of Arthur's methods to unitary groups

Abstract

In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.