A new proof of Jacquet-Rallis's fundamental lemma

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.

Streamlined proof avoiding to use the existence of smooth transfer and local relative trace formulas