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Abstract

We establish an explicit Plancherel decomposition for GLn(F)\GLn(E) where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai γ-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.

Details

Title
Plancherel formula for GLn(F)\GLn(E) and applications to the Ichino–Ikeda and formal degree conjectures for unitary groups
Author
Beuzart-Plessis Raphaël 1 

 Aix Marseille University, CNRS, Centrale Marseille, I2M, Marseille, France (GRID:grid.5399.6) (ISNI:0000 0001 2176 4817) 
Pages
159-297
Publication year
2021
Publication date
Jul 2021
Publisher
Springer Nature B.V.
ISSN
00209910
e-ISSN
14321297
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2539403473
Copyright
© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021.