The Whittaker Inversion Theorem and some applications

Nolan Wallach (UC San Diego)

26-Jan-2023, 22:00-23:00 (14 months ago)

Abstract: The Whittaker Plancherel theorem appeared as Chapter 15 in my two volume book, Real Reductive Groups. It was meant to be an application of Harish-Chandra’s Plancherel Theorem. As it turns out, there are serious gaps in the proof given in the books. At the same time as I was doing my research on the subject, Harish-Chandra was also working on it. His approach was very different from mine and appears as part of Volume 5 of his collected works; which consists of three pieces of research by Harish-Chandra that were incomplete at his death and organized and edited by Gangolli and Varadarajan. Unfortunately, it also does not contain a proof of the theorem. There was a complication in the proof of this result that caused substantial difficulties which had to do with the image of the analog of Harish-Chandra’s method of descent. In this lecture I will explain how one can complete the proof using a recent result of Raphael Beuzzart-Plessis. I will also give an application of the result to the Fourier transforms of automorphic functions at cusps.

(This seminar will be given remotely, but there will still be a live audience in the lecture room.)

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20pm


UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

Organizers: Kiran Kedlaya*, Alina Bucur, Aaron Pollack, Cristian Popescu, Claus Sorensen
*contact for this listing

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