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On the construction of monopoles for the classical groups. (English) Zbl 0682.32026
In recent years, magnetic monopoles have been extensively studied in at least three different ways, namely by a direct analytic approach, by twistor methods and by an extension, due to W. Nahm, of the ADHM construction for instantons. In the case when the gauge groups is SU(2), a detailed account of these methods and the relationship between them has been given by N. J. Hitchin [Commun. Math. Phys. 83, 579-602 (1982; Zbl 0502.58017); ibid. 89, 145-190 (1983; Zbl 0517.58014)]. The object of this paper is to extend these ideas to the other classical groups, establishing in each case an equivalence between three types of data, namely (A) generic monopoles with maximum symmetry breaking at infinity, (B) generic solutions of Nahm’s equations satisfying appropriate boundary conditions and (C) spectral data.
Reviewer: P.E.Newstead

MSC:
32L25 Twistor theory, double fibrations (complex-analytic aspects)
53C80 Applications of global differential geometry to the sciences
81T08 Constructive quantum field theory
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
53C05 Connections, general theory
20G45 Applications of linear algebraic groups to the sciences
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