Non-abelian Dyons

The dyonic quantum states of magnetic monopoles in Yang-Mills-Higgs theory with a non-abelian unbroken gauge group display a subtle interplay between magnetic and electric properties. This is described in detail in the theory with the gauge group SU(3) broken to U(2), and shown to be captured by the representation theory of the semi-direct product of U(2) with R^4. The implications of this observation for the fusion rules and electric-magnetic duality properties of dyonic states are pointed out.