  In this version referee's comments have been incorporated. Besides minor
corrections, new material has been added on irrational markings. To appear in
Ann. Inst. Fourier.
  We prove a condition for the existence of flat bundles on the punctured
two-sphere with prescribed holonomies around the punctures, involving
Gromov-Witten invariants of generalized flag varieties. This generalizes the
case of special unitary bundles described by S. Agnihotri and the second author
and independently P. Belkale.
