Abstract
We generalize the Shimura--Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group $\mathrm{M}\mathrm{p}_2$, to the metaplectic group $\mathrm{M}\mathrm{p}_{2n}$ 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.
Citation
Wee Teck Gan. Atsushi Ichino. "The Shimura–Waldspurger correspondence for $\mathrm{Mp}_{2n}$." Ann. of Math. (2) 188 (3) 965 - 1016, November 2018. https://doi.org/10.4007/annals.2018.188.3.5
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