Theta lifting for loop groups

TL;DR

This paper extends the classical theta lifting theory to loop groups, establishing a tower property, and constructs explicit nonvanishing cusp forms on these groups, advancing the understanding of automorphic forms in infinite-dimensional settings.

Contribution

It introduces a theta lifting framework for loop groups, extending classical results and providing the first explicit nonvanishing cusp forms in this context.

Findings

Extended the tower property to loop groups

Constructed explicit nonvanishing cusp forms on loop groups

Demonstrated applications to automorphic forms in infinite dimensions

Abstract

In this paper we study the theta lifting for loop groups and extend the classical tower property established by S. Rallis to the loop setting. As an application we obtain cusp forms on loop groups, and we give the first example where the cusp forms constructed using this method are nonvanishing.