On the Hyperk Ahler Metrics Associated to Singularities of Nilpotent Varieties
نویسندگان
چکیده
We study the hyperkk ahler metrics associated to minimal singularities in the nilpotent variety of a semisimple Lie group. We show that Kronheimer's 4-dimensional ALE spaces are naturally realized within the context of coadjoint orbits and can be thought of as certain moduli spaces of SU(2) invariant instantons on R 4 nf0g with appropriate boundary conditions. We also show that the hyperkk ahler metrics on the resolution of D 2 singularity arise within coadjoint orbits and that this has higher dimensional versions analogous to hyperkk ahler metrics on T C P n. We also give an explicit description of the hyperkk ahler metric on the orbit of highest root vectors and consequently an explicit description of 3-Sasakian homogeneous metrics.
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