Endoscopic Classification of Representations: Inner Forms of Unitary Groups

TL;DR

This paper classifies automorphic and irreducible admissible representations of non-quasi-split unitary groups, extending known classifications from quasi-split cases, using automorphic representations of general linear groups and Langlands parameters.

Contribution

It provides a new classification framework for non-quasi-split unitary groups based on existing results for quasi-split groups, linking automorphic and admissible representations.

Findings

Classification of automorphic representations via general linear groups

Classification of local admissible representations via Langlands parameters

Extension of known classifications to non-quasi-split unitary groups

Abstract

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split unitary groups. The classification of automorphic representations is given in terms of automorphic representations of general linear groups. The classification of irreducible admissible representations is given in terms of Langlands parameters.