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Monopoles and their spectral data. (English) Zbl 0708.58035
Summary: A new definition of spectral data of a monopole is given for any compact Lie or Kac-Moody group. It is shown that the spectral data determines the irreducible monopole. In the case of maximal symmetry breaking the spectral data is shown to reduce to an earlier definition in terms of algebraic curves indexed by the nodes of the Dynkin diagram of the group. The structure of solutions to Nahm’s equations corresponding to the monopole is discussed

MSC:
58Z05 Applications of global analysis to the sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81R40 Symmetry breaking in quantum theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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