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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-dualYang--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.

Maximally Non-Abelian Vortices from Self-dual Yang--Mills Fields