We consider in this work representations of the of the fundamental group of
the 3-punctured sphere in PU(2,1) such that the boundary loops are
mapped to PU(2,1). We provide a system of coordinates on the
corresponding representation variety, and analyse more specifically those
representations corresponding to subgroups of (3,3,β)-groups. In
particular we prove that it is possible to construct representations of the
free group of rank two \la a,b\ra in PU(2,1) for which a, b,
ab, abβ1, ab2, a2b and [a,b] all are mapped to parabolics.Comment: 21 pages, 11 figure