Green Functions Via Hyperbolic Localization

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

2010 Mathematics Subject Classification: Primary 20G05; Secondary 14F05, 32S60.

Keywords and Phrases: nilpotent cone; perverse sheaves; hyperbolic localization.

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