Affine Beilinson-Bernstein localization at the critical level

TL;DR

This paper proves a conjecture linking regular Kac-Moody representations at the critical level to eigensheaves on the affine Grassmannian, advancing the understanding of geometric representation theory.

Contribution

It establishes the Frenkel-Gaitsgory localization conjecture at the critical level using categorical Moy-Prasad theory, extending prior results.

Findings

Proves the Frenkel-Gaitsgory localization conjecture.

Connects Kac-Moody representations to eigensheaves on the affine Grassmannian.

Utilizes categorical Moy-Prasad theory for the proof.

Abstract

We prove the Frenkel-Gaitsgory localization conjecture describing regular Kac-Moody representations at critical level via eigensheaves on the affine Grassmannian using categorical Moy-Prasad theory. This extends previous work of the authors.