  Consider an algebraic action of a connected complex reductive algebraic group
on a complex polarized projective variety. In this paper, we first introduce
the nilpotent quotient, the quotient of the polarized projective variety by a
maximal unipotent subgroup. Then, we introduce and investigate three induced
actions: one by the reductive group, one by a Borel subgroup, and one by a
maximal torus, respectively. Our main result is that there are natural
correspondences among quotients of these three actions. In the end, we mention
a possible application to the moduli spaces of parabolic bundles over algebraic
curves for further research.
