The Gross-Prasad conjecture and local theta correspondence

• 成果类型: Article
• 署名作者: Gan, Wee Teck; Ichino, Atsushi
• 署名单位: National University of Singapore; Kyoto University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0662-8
• 发表日期: 2016
• 页码: 705-799
• 关键词: p-adic groups; series; REPRESENTATIONS; dichotomy; FORMULA; PROOF; gl(n)

摘要

We establish the Fourier-Jacobi case of the local Gross-Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier-Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence. The proof uses Arthur's multiplicity formula and thus is one of the first examples of a concrete application of this global reciprocity law.