  Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic
action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup
of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical
invariants for such triples $(F,\alpha,K)$. The invariants are associated with
moduli spaces of solutions of a certain vortex type equation on a Riemann
surface.
  We give explicite descriptions of the moduli spaces associated with the
triple $(\Hom(\C^r,\C^{r_0}), \alpha_{\rm can},U(r))$, where $\alpha_{\rm can}$
denotes the canonical action of $\hat K=U(r)\times U(r_0)$ on
$\Hom(\C^r,\C^{r_0})$. In the abelian case $r=1$, the new invariants can be
computed expliciteley and identified with the full Seiberg-Witten invariants of
ruled surfaces.
