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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 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.

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up vote 7 down vote accepted

This is answered (except for a few cases in $E_7$ and $E_8$) in: Baohua Fu, Symplectic Resolutions for Nilpotent Orbits.

Maybe it's worth mentioning: orbits which are the image of $T^*(G/P)$ for some $P$ are called Richardson and are relatively easy to understand. The tricky part is know when that map is a resolution, since in many cases (outside type A) it is finite to 1 instead. One useful criterion is that it will be a resolution it the orbit is simply connected.

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