  The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills
theory on a spatial three-torus contains a certain number of bound states,
characterized by their discrete abelian magnetic and electric 't Hooft fluxes.
At weak coupling, the wave-functions of these states are supported near points
in the moduli space of flat connections where the unbroken gauge group is
semi-simple. The number of such states is related to the number of normalizable
bound states at threshold in the supersymmetric matrix quantum mechanics with
16 supercharges based on this unbroken group. Mathematically, the determination
of the spectrum relies on the classification of almost commuting triples with
semi-simple centralizers. We complete the work begun in a previous paper, by
computing the spectrum of bound states in theories based on the
even-dimensional spin groups and the exceptional groups. The results satisfy
the constraints of S-duality in a rather non-trivial way.
