Transfer to Characteristic Zero of the Jacquet–Mao’s Metaplectic Fundamental Lemma

Source abstract

Abstract Jacquet conjectured that globally a cuspidal automorphic representation of $\mathrm{G}\mathrm{L}_r$ 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.