Endoscopic Classification of Representations: Inner Forms of Unitary Groups

2014/09/12 by Tasho Kaletha, Alberto Mínguez, Kaletha, Tasho +5 · 5 citations
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1409.3731

openalex publication_date 2014/09/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Cited by

• The local Langlands conjecture
• 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
• Affine Hecke algebras for classical p-adic groups

Related

• Endoscopic classification of representations of quasi-split unitary\n groups
• Nonarchimedean components of non-endoscopic automorphic representations for quasisplit Sp(N) and O(N)
• Raising the level of automorphic representations of GL_2n of unitary type
• Endoscopic classification of very cuspidal representations of quasi-split unitary groups
• The endoscopic classification of representations of non-quasi-split odd special orthogonal groups