We give a new proof of the so-called Lie algebra version of the Jacquet–Rallis fundamental lemma for local non-Archimedean fields of characteristic 0. This proof is local and based on a previous result of Zhang on the compatibility of smooth transfer with a (partial) Fourier transform.
"A new proof of the Jacquet–Rallis fundamental lemma." Duke Math. J. 170 (12) 2805 - 2814, 1 September 2021. https://doi.org/10.1215/00127094-2020-0090