On the Whittaker Plancherel Theorem for Real Reductive Groups
Representation Theory
2023-10-31 v9
Abstract
The purpose of this article is to give the first complete proof of the Whittaker Plancherel Theorem. The proof uses Harish-Chandra's Plancherel Theorem for a real reductive group and its exposition can be used as an introduction to Harish-Chandra's ideas. The proof follows the basic ideas in the author's original attempt in his second volume on real reductive groups. An error in the calculation of the Whittaker Transform of a Harish-Chandra wave packet is fixed using a result of Rapha\"el Beuzart-Plessis.
Cite
@article{arxiv.1705.06787,
title = {On the Whittaker Plancherel Theorem for Real Reductive Groups},
author = {Nolan R. Wallach},
journal= {arXiv preprint arXiv:1705.06787},
year = {2023}
}
Comments
This is the tenth and final version of this paper. It supersedes all of the earlier versions and gives a complete proof of the theorem. It also fixes a gap in the previous version involving j_{\sigma,\nu}