Twisted global section functor for D-modules on affine Grassmannian

TL;DR

This paper constructs a twisted global section functor for critical twisted D-modules on the affine Grassmannian, proving its exactness and faithfulness, thus generalizing previous work to arbitrary weights.

Contribution

It introduces a new twisted global section functor for all integral dominant weights, extending the results of Frenkel and Gaitsgory beyond the zero weight case.

Findings

The functor is exact.

The functor is faithful.

Generalization of previous results to all weights.

Abstract

For each integral dominant weight $\lambda$, we construct a twisted global section functor $\Gamma^{\lambda}$ from the category of critical twisted $D$-modules on affine Grassmannian to the category of $\lambda$-regular modules of affine Lie algebra at critical level. We proved that $\Gamma^{\lambda}$ is exact and faithful. This generalized the work of Frenkel and Gaitsgory in the case when $\lambda=0$.