REPRESENTATIONS OF FUNDAMENTAL-GROUPS WHOSE HIGGS BUNDLES ARE PULLBACKS

The representations of the fundamental group of a smooth projective va riety into a complex simple group are discussed in terms of the corres ponding Higgs bundles. A necessary and sufficient condition is found f or a representation to factor geometrically through the fundamental gr oup of an orbicurve. The factorization question is studied further for the case of higher dimensional target varieties.