Splitting metaplectic cover groups

Abstract

If $(G_1,G_2)$ is a dual reductive pair of type I in $Sp(W)$, it is known that the degree $8$ metaplectic cover of $Sp(W)$ splits over $G_1{G}_2$, with one obvious exception. In this paper we replace $G_1{G}_2$ by a larger subgroup obtained via similitude groups, and show that the degree $8$ metaplectic cover splits, with the same obvious exception.

17 pages, a revised version