  The character varieties of representations of a surface group into the Lie
groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of
the moduli space of Higgs bundles. We show that the fibres of the integrable
system in these cases are not abelian varieties, but are instead moduli spaces
of rank 2 bundles on a spectral curve, satisfying natural stability conditions.
