The Shimura-Waldspurger correspondence for Mp(2n)

TL;DR

This paper explores recent advances and conjectures in the representation theory and automorphic forms of the metaplectic group Mp(2n), focusing on the theta correspondence, endoscopy, and trace formula techniques.

Contribution

It formulates new conjectures and discusses developments in the genuine representation theory of Mp(2n) related to automorphic forms and the theta correspondence.

Findings

Descriptions of recent developments in the theory

Formulation of new conjectures in automorphic forms

Insights into the theta correspondence and endoscopy

Abstract

We describe some recent developments and formulate some conjectures in the genuine representation theory and the study of automorphic forms of the metaplectic group $\mathrm{Mp}(2n)$, from the point of view of the theta correspondence as well as from the point of view of the theory of endoscopy and the trace formula.