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Peter Crooks
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Let $G$ be a connected, simply-connected complex semisimple group. We have the famous Springer resolution $$T^*(G/B)\rightarrow\mathcal{N}$$ of the closure of the regular nilpotent orbit. My understanding is that the closures of only some nilpotent $G$-orbits $\mathcal{O}$ admit symplectic resolutions $$T^*(G/P)\rightarrow\overline{\mathcal{O}}.$$$$T^*(G/P)\rightarrow\overline{\mathcal{O}}$$ when $G=SL_n(\mathbb{C})$, but that this need not be the case for other $G$. Accordingly, I am looking for a reference giving some information as to which nilpotent orbits have their closures resolved in this way. In particular, do all nilpotent $SL_n(\mathbb{C})$-orbit closures admit such resolutions?

Let $G$ be a connected, simply-connected complex semisimple group. We have the famous Springer resolution $$T^*(G/B)\rightarrow\mathcal{N}$$ of the closure of the regular nilpotent orbit. My understanding is that the closures of only some nilpotent $G$-orbits $\mathcal{O}$ admit symplectic resolutions $$T^*(G/P)\rightarrow\overline{\mathcal{O}}.$$ Accordingly, I am looking for a reference giving some information as to which nilpotent orbits have their closures resolved in this way. In particular, do all nilpotent $SL_n(\mathbb{C})$-orbit closures admit such resolutions?

Let $G$ be a connected, simply-connected complex semisimple group. We have the famous Springer resolution $$T^*(G/B)\rightarrow\mathcal{N}$$ of the closure of the regular nilpotent orbit. My understanding is that the closures of nilpotent $G$-orbits $\mathcal{O}$ admit symplectic resolutions $$T^*(G/P)\rightarrow\overline{\mathcal{O}}$$ when $G=SL_n(\mathbb{C})$, but that this need not be the case for other $G$. Accordingly, I am looking for a reference giving some information as to which nilpotent orbits have their closures resolved in this way.

Source Link
Peter Crooks
  • 4.9k
  • 2
  • 22
  • 42

Which nilpotent orbit closures admit Springer resolutions?

Let $G$ be a connected, simply-connected complex semisimple group. We have the famous Springer resolution $$T^*(G/B)\rightarrow\mathcal{N}$$ of the closure of the regular nilpotent orbit. My understanding is that the closures of only some nilpotent $G$-orbits $\mathcal{O}$ admit symplectic resolutions $$T^*(G/P)\rightarrow\overline{\mathcal{O}}.$$ Accordingly, I am looking for a reference giving some information as to which nilpotent orbits have their closures resolved in this way. In particular, do all nilpotent $SL_n(\mathbb{C})$-orbit closures admit such resolutions?