Local theta correspondence of tempered representations and Langlands parameters

• 成果类型: Article
• 署名作者: Atobe, Hiraku; Gan, Wee Teck
• 署名单位: University of Tokyo; National University of Singapore
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0730-8
• 发表日期: 2017
• 页码: 341-415
• 关键词: gross-prasad conjecture; special orthogonal groups; fourier-jacobi periods; p-adic groups; discrete-series; metaplectic groups; howe correspondence; fundamental lemma; integral formula; unitary groups

摘要

In this paper, we give an explicit determination of the theta lifting for symplectic-orthogonal and unitary dual pairs over a nonarchimedean field F of characteristic 0. We determine when theta lifts of tempered representations are nonzero, and determine the theta lifts in terms of the local Langlands correspondence.