A new proof of Jacquet-Rallis's fundamental lemma

TL;DR

This paper presents a novel proof of the Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero, utilizing Fourier transform techniques and previous compatibility results.

Contribution

It introduces a new local proof of the fundamental lemma, building on W. Zhang's work on smooth transfer and Fourier transform compatibility.

Findings

Provides a new proof of the fundamental lemma in the Lie algebra setting.

Utilizes Fourier transform methods to establish the lemma.

Builds on previous results by W. Zhang for compatibility of smooth transfer.

Abstract

We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on a previous result of W. Zhang on the compatibility of smooth transfer with a (partial) Fourier transform.