Endoscopic classification of representations of quasi-split unitary groups

2012/06/05 by Chung Pang Mok, Mok, Chung Pang · 7 citations
Mathematics · #11R42 (Secondary) #22E50 (Primary) 20G35 #22E55 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11R42 #msc:20G35 #msc:22E50 #msc:22E55

paper · pdf · doi:10.48550/arxiv.1206.0882

274 pages

openalex publication_date 2012/06/05 · arxiv created 2013/06/22 · arxiv updated 2013/06/25 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28

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.

Cited by

• The local Langlands conjecture
• Algebraicity of adjoint L-functions for quasi-split groups
• Factorization of periods, construction of automorphic motives and Deligne's conjecture over CM-fields
• The square-integrability of double descent
• The Kodaira dimension of even-dimensional ball quotients
• Motives and Automorphic Representations
• L-packets and the generic Arthur packet conjectures for even unitary similitude groups

Related

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• The endoscopic classification of representations of non-quasi-split odd special orthogonal groups
• Endoscopic classification of very cuspidal representations of quasi-split unitary groups
• Endoscopy and the automorphic tensor product on the unitary group
• Nonarchimedean components of non-endoscopic automorphic representations for quasisplit Sp(N) and O(N)