The Shimura-Waldspurger correspondence for ${\mathrm{Mp}}_{2n}$

Abstract

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group ${\mathrm{Mp}}_2$, to the metaplectic group ${\mathrm{Mp}}_{2n}$ of higher rank. To establish this, we transport Arthur's endoscopic classification of representations of the odd special orthogonal group ${\mathrm{SO}}_{2r+1}$ with $r\gg 2n$ by using a result of J. S. Li on global theta lifts in the stable range.