  A particular dimensional reduction of SU(2N) Yang--Mills theory on $\Sigma
\times S^2$, with $\Sigma$ a Riemann surface, yields an $S(U(N) \times U(N))$
gauge theory on $\Sigma$, with a matrix Higgs field. The SU(2N) self-dual
Yang--Mills equations reduce to Bogomolny equations for vortices on $\Sigma$.
These equations are formally integrable if $\Sigma$ is the hyperbolic plane,
and we present a subclass of solutions.
