  Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The
symmetric spaces associated to these G's are the classical bounded symmetric
domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using
the correspondence between representations of fundamental groups of K\"{a}hler
manifolds and Higgs bundles we study representations of uniform lattices of
SU(m,1), m>1, into G. We prove that the Toledo invariant associated to such a
representation satisfies a Milnor-Wood type inequality and that in case of
equality necessarily G=SU(p,2) with p>=2m and the representation is reductive,
faithful, discrete, and stabilizes a copy of complex hyperbolic space (of
maximal possible induced holomorphic sectional curvature) holomorphically and
totally geodesically embedded in the Hermitian symmetric space
SU(p,2)/S(U(p)xU(2)), on which it acts cocompactly.
