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Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. (English) Zbl 0826.17026
This paper studies certain hyper-Kähler quotients of representation spaces of quivers on graphs (which the author calls quiver varieties). These include the ALE spaces constructed as hyper-Kähler quotients by P. B. Kronheimer [J. Differ. Geom. 29, No. 3, 665–683 (1989; Zbl 0671.53045)] and are related to the work of A. D. King [Q. J. Math., Oxf. II. Ser. 45, No. 180, 515–530 (1994; Zbl 0837.16005)].
The author considers their geometry, topology, singularities and natural \(C^*\)-actions, and looks at a number of examples.

MSC:
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
53C55 Global differential geometry of Hermitian and Kählerian manifolds
16G20 Representations of quivers and partially ordered sets
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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