Plancherel formula for GLn(F)\GLn(E) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups
成果类型：
Article
署名作者：
Beuzart-Plessis, Raphael
署名单位：
Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-021-01032-6
发表日期：
2021
页码：
159-297
关键词：
摘要：
We establish an explicit Plancherel decomposition for GL(n)(F)\GL(n)(E) where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai gamma-factors. We also give two applications of this Plancherel formula: first to the global Ichino-Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by Zhang (J Am Math Soc 27:541-612, 2014) and secondly to the Hiraga-Ichino-Ikeda conjecture on formal degrees (J Am Math Soc 21(1):283-304, 2008) in the case of unitary groups.