On the hyperkähler metrics associated to singularities of nilpotent varieties (Q1916020)

Let \(G\) be a complex, semisimple Lie group, and \(N\) the nilpotent variety in the Lie algebra of \(G\). The hyperkähler metrics associated to minimal singularities in the nilnotent variety are studied in this paper. Kronheimer's 4-dimensional ALE (Asymptotically Locally Euclidean) spaces are naturally realized within the context of coadjoint orbits and are identified as certain moduli spaces of SU(2)-invariant instantons on \(\mathbb{R}^k\setminus\{0\}\) with appropriate boundary conditions. The author also shows that the hyperkähler metrics on the resolution of the \(D_2\) singularity arise within coadjoint orbits. The author further gives the description of the hyperkähler metric on the orbit of highest root vectors.