Abstract. We study the precise structure of Hilbert scheme Hilb G (C 3 ) of G-orbits in the space C 3 when the group G is a simple subgroup of SL(3, C) of either 60 or 168. These are the only possible non-abelian simple subgroups of SL(3, C).
Abstract. For most of the finite subgroups of SL(3, C) we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae [McKay99] for subgroups of SU(2). We also study the G-orbit Hilbert scheme Hilb G (C 3 ) for any finite subgroup G of SO (3), which is known to be a minimal (crepant) resolution of the orbit space C 3 /G. In this case the fiber over the origin of the Hilbert-Chow morphism from Hilb G (C 3 ) to C 3 /G consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of G. This is an SO(3) version of the McKay correspondence in the SU(2) case.
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