Abstract
We study the hyperkähler 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 ofSU(2) invariants instantons on ℝ4∖{O} with appropriate boundary conditions.
We also show that the hyperkähler metrics on the resolution of theD 2 singularity arise within coadjoint orbits and that this has higher dimensional versions analogous to hyperkähler metrics onT *ℂP n. We also give an explicit description of the hyperkähler metric on the orbit of highest root vectors and, consequently, an explicit description of 3-Sasakian homogeneous metrics.
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Communicated by S. Salamon
Research supported by a Postdoctoral Fellowship from the Natural Sciences and Engineering Council of Canada
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Bielawski, R. On the hyperkähler metrics associated to singularities of nilpotent varieties. Ann Glob Anal Geom 14, 177–191 (1996). https://doi.org/10.1007/BF00127972
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DOI: https://doi.org/10.1007/BF00127972