  We propose an electric-magnetic symmetry group in non-abelian gauge theory,
which we call the skeleton group. We work in the context of non-abelian
unbroken gauge symmetry, and provide evidence for our proposal by relating the
representation theory of the skeleton group to the labelling and fusion rules
of charge sectors. We show that the labels of electric, magnetic and dyonic
sectors in non-abelian Yang-Mills theory can be interpreted in terms of
irreducible representations of the skeleton group. Decomposing tensor products
of these representations thus gives a set of fusion rules which contain
information about the full fusion rules of these charge sectors. We demonstrate
consistency of the skeleton's fusion rules with the known fusion rules of the
purely electric and purely magnetic magnetic sectors, and extract new
predictions for the fusion rules of dyonic sectors in particular cases. We also
implement S-duality and show that the fusion rules obtained from the skeleton
group commute with S-duality.
