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

## TL;DR

This paper extends the Shimura-Waldspurger correspondence from the metaplectic group rac{1}{2} to higher rank groups rac{n}{2}, utilizing Arthur's classification and theta lift techniques.

## Contribution

It generalizes the correspondence to rac{n}{2} for higher rank metaplectic groups using endoscopic classification and theta lifts.

## Key findings

- Established the correspondence for rac{n}{2} in higher rank cases.
- Connected Arthur's classification with theta lift results.
- Provided a framework for understanding automorphic spectra of rac{n}{2}.

## 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.