Symplectic resolution conjecture for coverings of nilpotent orbit closures

Let pˉ:X\0\bar{p}: X \rightarrow \overline{\0} be a covering of a nilpotent orbit in a simple Lie algebra g\mathfrak{g} such that R[1]=0R[1]=0. Suppose that π:ZX\pi: Z\rightarrow X is a symplectic resolution. Let g=R[2]\mathfrak{g}'=R[2] and let GG' be the simply connected Lie group with Lie algebra g\mathfrak{g}'. The symplectic resolution conjecture. There exists a parabolic subgroup PP' of GG' such that ZZ is isomorphic to T(G/P)T^*(G'/P'), and under this isomorphism the map π\pi becomes

T(G/P)X.T^*(G'/P')\rightarrow X.

The conjecture predicts that every symplectic resolution in the case R[1]=0R[1]=0 is a cotangent-bundle resolution associated with a parabolic subgroup of GG'. The supplied status evidence indicates that the claim has been resolved; the source context discusses the classification of symplectic resolutions for coverings of nilpotent orbit closures.

Sources & referencesView supporting material

Primary source

Baohua Fu, “Symplectic Resolutions for Coverings of Nilpotent Orbits”, arXiv:math/0212024 (2002).

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