The Plancherel formula for $L^2(GL_n(F)\backslash GL_n(E))$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups

Workshop on Representation Theory and Analysis on Locally Symmetric Spaces
Topic:The Plancherel formula for $L^2(GL_n(F)\backslash GL_n(E))$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups
Speaker:Raphael Beuzart-Plessis
Affiliation:Centre national de la recherche scientifique
Date:Tuesday, March 6
Time/Room:11:30am - 12:30pm/Simonyi Hall 101
Video Link:https://video.ias.edu/RepTheoryAnalysisLocallySymmetricSpaces/2018/0306-RaphaelBeuzart-Plessis

Abstract : Let $E/F$ be a quadratic extension of local fields of characteristic zero. In this talk, I will explain two ways to compute the Plancherel decomposition of $L^2(GL_n(F)\backslash GL_n(E))$. In both cases, the result involves the image of base change from unitary groups to $GL_n(E)$ and is in accordance with a general conjecture of Sakellaridis-Venkatesh on the spectral decomposition of spherical varieties. We will also give applications of our formulas to the so-called Ichino-Ikeda and formal degree conjectures for unitary groups.