Transfer to Characteristic Zero of the Jacquet-Mao's Metaplectic Fundamental Lemma

Jacquet conjectured that globally a cuspidal automorphic representation of GL(r) should be in the image of the metaplectic correspondence precisely when it is distinguished with respect to a split orthogonal similitude group. Jacquet-Mao have suggested an approach to solve this problem by using "relative" traces formula. One of the steps of this approach is the Jacquet-Mao's metaplectic fundamental lemma. The author proved this fundamental lemma for any r in the case of positive characteristic. The aim of this paper is to extend this result to the more general case.