Local Langlands Correspondence for Unitary Groups via Theta Lifts

2020/08/04 by Rui Chen, Chen, Rui, Jialiang Zou +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.2008.01771

arXiv admin note: text overlap with arXiv:1409.6824 by other authors

openalex publication_date 2020/08/04 · arxiv created 2021/10/10 · arxiv updated 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence, which was established in an early paper of Mok) to non quasi-split unitary groups. We also prove that our classification satisfies some good properties, which characterize it uniquely. In particular, this provides an alternative approach to the works of Kaletha-Minguez-Shin-White and Moeglin-Renard.

Citations

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• Theta correspondences for GSp(4)
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• The Gross-Prasad conjecture and local theta correspondence

Cited by

• The local Langlands conjecture
• The Kodaira dimension of even-dimensional ball quotients

Related

• Depth preserving property of the local Langlands correspondence for non-quasi-split unitary groups
• Theta correspondence for almost unramified representations of unitary groups
• Local Langlands correspondence in rigid families
• Genericity and contragredience in the local Langlands correspondence
• Compatibility of the Fargues--Scholze correspondence for unitary groups