We prove both the group version and the Lie algebra version of the fundamental lemma appearing in a relative trace formula of Jacquet and Rallis in the function field case when the characteristic is greater than the rank of the relevant groups. In the appendix by Gordon, our results are transferred to the -adic field case, for sufficiently large .
"The fundamental lemma of Jacquet and Rallis." Duke Math. J. 156 (2) 167 - 227, 1 February 2011. https://doi.org/10.1215/00127094-2010-210