Geodesic
The Shimura–Waldspurger correspondence for $\mathrm {Mp}_{2n}$
Wee Teck Gan1 ; Atsushi Ichino2
1 Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
2 Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
Annals of mathematics, Tome 188 (2018) no. 3, pp. 965-1016

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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.

DOI : 10.4007/annals.2018.188.3.5

Wee Teck Gan 1 ; Atsushi Ichino 2

1 Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076
2 Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan 
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Wee Teck Gan; Atsushi Ichino. The Shimura–Waldspurger correspondence for $\mathrm  {Mp}_{2n}$. Annals of mathematics, Tome 188 (2018) no. 3, pp. 965-1016. doi: 10.4007/annals.2018.188.3.5

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