English

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

Number Theory 2018-08-06 v3 Representation Theory

Abstract

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group Mp2\mathrm{Mp}_2, to the metaplectic group Mp2n\mathrm{Mp}_{2n} of higher rank. To establish this, we transport Arthur's endoscopic classification of representations of the odd special orthogonal group SO2r+1\mathrm{SO}_{2r+1} with r2nr \gg 2n by using a result of J. S. Li on global theta lifts in the stable range.

Keywords

Cite

@article{arxiv.1705.10106,
  title  = {The Shimura-Waldspurger correspondence for $\mathrm{Mp}_{2n}$},
  author = {Wee Teck Gan and Atsushi Ichino},
  journal= {arXiv preprint arXiv:1705.10106},
  year   = {2018}
}
R2 v1 2026-06-22T20:02:00.471Z