Whittaker coefficients of geometric Eisenstein series

TL;DR

This paper proves a geometric Langlands conjecture relating Whittaker coefficients of Eisenstein series to functions on moduli spaces by using factorization and chiral homology techniques.

Contribution

It provides a rigorous proof of the geometric Langlands prediction by connecting Whittaker coefficients with factorization homology and chiral algebra methods.

Findings

Established the isomorphism predicted by geometric Langlands.

Connected Whittaker coefficients to factorization homology.

Applied Beilinson and Drinfeld's formula for chiral homology.

Abstract

Geometric Langlands predicts an isomorphism between Whittaker coefficients of Eisenstein series and functions on the moduli space of $\check{N}$-local systems. We prove this formula by interpreting Whittaker coefficients of Eisenstein series as factorization homology and then invoking Beilinson and Drinfeld's formula for chiral homology of a chiral enveloping algebra.