The Shimura-Waldspurger correspondence for Mp2n

• 成果类型: Article
• 署名作者: Gan, Wee Teck; Ichino, Atsushi
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.188.3.5
• 发表日期: 2018
• 页码: 965-1016
• 关键词: local theta-correspondence; half integral weight; gross-prasad conjecture; automorphic l-functions; p-adic groups; classical-groups; unitary representations; irreducible representations; langlands correspondence; metaplectic groups

摘要

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group Mp(2), to the metaplectic group Mp(2n) of higher rank. To establish this, we transport Arthur's endoscopic classification of representations of the odd special orthogonal group SO2r+1 with r >> 2n by using a result of J.-S. Li on global theta lifts in the stable range.