Dimensional reduction and moment maps

@inproceedings{Nagatomo2002DimensionalRA,
  title={Dimensional reduction and moment maps},
  author={Yasuyuki Nagatomo},
  year={2002}
}
Abstract We give a unified viewpoint of moment maps in the case of symplectic, hyper-Kahler, quaternion-Kahler and holomorphic contact manifolds. The Higgs field can be regarded as a moment map under some additional conditions in each case. Using dimensional reductions and moment maps, we reduce the standard 1 instanton on H P 1 ≅S 4 to an SO(3) instanton on C P 1 × C P 1 and the standard 1 instanton on H P n to the standard 1 instanton on Gr 2 ( C n+1 ) .