On the construction of monopoles for the classical groups |
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| Authors: | Jacques Hurtubise Michael K. Murray |
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| Affiliation: | 1. School of Mathematics, Institute for Advanced Study, 08540, Princeton, N.J., USA
2. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke St. W., H3A 2K6, Montreal, Quebec, Canada
3. Department of Mathematics. R.S. Phys. S., The Australian National University, GPO Box 4, 2601, Canberra, ACT, Australia
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| Abstract: | ForG a classical group, an equivalence is exhibited between:| A) | G monopoles over  3, with maximal symmetry breaking at infinity, | | B) | families of (rank (G)) algebraic curves inT 1, along with divisors on those curves, satisfying certain constraints, | | C) | solutions of Nahm's equations over (rank(G)) intervals, satisfying the appropriate boundary conditions. |
A) and B) are linked by twistor techniques, B) and C) via the Krichever method for solving non-linear differential equations, and A) and C) via the ADHMN construction, providing a unified picture of techniques for solution. Amongst other things, an asymptotic formula for the Higgs field of the monopole is computed.Communicated by A. Jaffe |
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