  Many properties of the moduli space of abelian vortices on a compact Riemann
surface are known. For non-abelian vortices the moduli space is less well
understood. Here we consider non-abelian vortices on the Riemann sphere CP^1,
and we study their moduli spaces near the Bradlow limit. We give an explicit
description of the moduli space as a Kahler quotient of a finite-dimensional
linear space. The dimensions of some of these moduli spaces are derived.
Strikingly, there exist non-abelian vortex configurations on CP^1, with
non-trivial vortex number, for which the moduli space is a point. This is in
stark contrast to the moduli space of abelian vortices. For a special class of
non-abelian vortices the moduli space is a Grassmannian, and the metric near
the Bradlow limit is a natural generalization of the Fubini--Study metric on
complex projective space. We use this metric to investigate the statistical
mechanics of non-abelian vortices. The partition function is found to be
analogous to the one for abelian vortices.
