Construction of Nahm data and BPS monopoles with continuous symmetries

We study solutions to Nahm's equations with continuous symmetries and, under certain (mild) hypotheses, we classify the corresponding Ans\"atze. Using our classification, we construct novel Nahm data, and prescribe methods for generating further solutions. Finally, we use these results to construct new BPS monopoles with spherical symmetry.Comment: 36 pages, 1 table, 2 figures, published versio