Green functions via hyperbolic localization

Abstract

Let $G$ be a reductive algebraic group, with nilpotent cone $\mathcal{N}$ and flag variety $\mathcal{B}$. We construct an exact functor from perverse sheaves on $\mathcal{N}$ to locally constant sheaves on $\mathcal{B}$, and we use it to study Ext-groups and stalks of simple perverse sheaves on $\mathcal{N}$ in terms of the cohomology of $\mathcal{B}$.