  In this work, we consider relative character varieties for representations of
the 3-punctured sphere group in PU(2,1). We provide necessary and sufficient
conditions on the peripheral conjugacy classes, for such a representation to
admit a decomposition as products of special elliptic elements. We prove that
the representations satisfying these conditions form fibers of the so-called
momentum map for PU(2,1). We apply these results to representations of the even
subgroup of triangle groups, and describe components of the associated
character variety.
