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Cartan decomposition of the moment map. (English) Zbl 1110.32008
The aim of the paper is to develop a geometric invariant theory for actions of real Lie groups on complex spaces. The authors accomplish this for certain real subgroups of a complex reductive group. The reductive group acts holomorphically on a complex space \(Z\). Assuming that \(Z\) admits an invariant Kähler structure and an equivariant moment mapping, they study the properties of an asociated moment mapping and consider its fibers and associated notions of semistable points. They also consider several topics pertaining to proper actions and compact isotropy groups. The results on proper actions are applied to obtain decompositions for groups and homogeneous spaces. The application relies on properties of distinguished strictly plurisubharmonic exhaustion.

32M05 Complex Lie groups, group actions on complex spaces
57S20 Noncompact Lie groups of transformations
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