Abstract
The problem of classifying the reduced phase spaces of the natural torus action on a generic coadjoint orbit of SU(n) is considered. The concept of a stratified fibre bundle is defined. It is proved that the orbit map of an equivariant fibre bundle is a stratified fibre bundle. This result is then used to give an iterative description of the reduced phase spaces of the torus action on a generic coadjoint orbit of SU(n). The theory is illustrated with a detailed examination of the n = 3 case, that of the two torus action on a coadjoint orbit of SU(3).