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


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.


Wee Teck Gan

Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076

Atsushi Ichino

Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan