On the construction of monopoles for the classical groups (Q1824074): Difference between revisions

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 \textit{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.