A Question on Splitting of Metaplectic Covers

Abstract

Abstract. Let E/F be a quadratic extension of a non-Archimedian local field. Splitting of the 2-fold metaplectic cover of Sp 2n (F) when restricted to various subgroups of Sp 2n (F) plays an important role in application of the Weil representation of the metaplectic group. In this paper we prove the splitting of the metaplectic cover of GL 2 (E) over the subgroups GL 2 (F) and D × F , where D F is the quaternion division algebra with center F, as a first step in our study of the restriction of representations of metaplectic cover of GL 2 (E) to GL 2 (F) and D × F . These results were suggested to the author by Professor Dipendra Prasad.