On Harish-Chandra's Plancherel theorem for Riemannian symmetric spaces

TL;DR

This paper reviews the Plancherel theory for Riemannian symmetric spaces, illustrating modern methods and explaining how Harish-Chandra's theorem can be derived using these approaches.

Contribution

It provides an overview of recent developments in Plancherel theory for symmetric spaces and demonstrates their application to Harish-Chandra's theorem.

Findings

Modern methods in Plancherel theory are applicable to symmetric spaces.

Harish-Chandra's theorem can be proven using these new methods.

The paper clarifies the connection between recent techniques and classical results.

Abstract

In this article we give an overview of the Plancherel theory for Riemannian symmetric spaces Z = G/K. In particular we illustrate recently developed methods in Plancherel theory for real spherical spaces by explicating them for Riemannian symmetric spaces, and we explain how Harish-Chandra's Plancherel theorem for Z can be proven from these methods.