Twisted global section functor for D-modules on affine Grassmannian
  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 $\lambda=0$. 
Tsao-Hsien Chen, Giorgia Fortuna
math.RT