SYMMETRICAL MONOPOLES

We discuss SU(2) Bogomolny monopoles of arbitrary charge k invariant u nder various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We consider monopoles invariant under inversion in a p lane, monopoles with cyclic symmetry, and monopoles having the symmetr y of a regular solid. We introduce the notion of a strongly centred mo nopole and show that the space of such monopoles is a geodesic submani fold of the monopole moduli space. By solving Nahm's equations we prov e the existence of a tetrahedrally symmetric monopole of charge 3 and an octahedrally symmetric monopole of charge 4, and determine their sp ectral curves. Using the geodesic approximation to analyse the scatter ing of monopoles with cyclic symmetry, we discover a novel type of non -planar k-monopole scattering process.