On the Siegel-Weil Theorem for Loop Groups (I)

TL;DR

This paper establishes a new Siegel-Weil formula for orthogonal and symplectic groups, laying the groundwork for future generalizations to loop groups, advancing the understanding of automorphic forms and representation theory.

Contribution

It introduces a novel Siegel-Weil formula for classical groups, providing a key step toward extending the theory to loop groups.

Findings

Proved a new Siegel-Weil formula for orthogonal groups

Extended the formula to symplectic groups

Set the stage for generalization to loop groups

Abstract

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.