Semisimple Lie groups satisfy property RD, a short proof

TL;DR

This paper provides a concise, elementary proof demonstrating that connected semisimple real Lie groups possess property RD, utilizing a linearization approach to simplify the proof process.

Contribution

It introduces a simplified, elementary proof of property RD for semisimple Lie groups, avoiding complex prior methods.

Findings

Connected semisimple real Lie groups satisfy property RD

The proof is based on a linearization technique

The approach simplifies existing proofs of property RD

Abstract

We give a short elementary proof of the fact that connected semisimple real Lie groups satisfy property RD. The proof is based on a process of linearization.