We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions of a system of nonlinear first order elliptic partial differential equations in the ambient symplectic manifold. The symplectic manifold carries a Hamiltonian group action. The equations involve the Cauchy-Riemann operator over a Riemann surface, twisted by a connection, and couple the curvature of the connection with the moment map. Our work should prove a conjecture that the genus zero invariants of Hamiltonian group actions defined by these equations agree with the genus zero Gromov-Witten invariants of the symplectic quotient in the monotone case.