  In this paper, we study the dynamics of a general class of antiholomorphic
correspondences; i.e., multi-valued maps with antiholomorphic local branches,
on the Riemann sphere. Such correspondences are closely related to a class of
single-valued antiholomorphic maps in one complex variable; namely, Schwarz
reflection maps of simply connected quadrature domains. Using this connection,
we prove that matings of all parabolic antiholomorphic rational maps with
connected Julia sets (of arbitrary degree) and antiholomorphic analogues of
Hecke groups can be realized as such correspondences. We also draw the same
conclusion when parabolic maps are replaced with critically non-recurrent
antiholomorphic polynomials with connected Julia sets.
