Complex geometry of actions and related representations

• Applicant: Professor Dr. Peter Heinzner
• Subject Area: Mathematics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 125746602

The interplay between actions of a given group on geometric objects having rich structure and linear representations on associated function spaces is studied. The groups being considered are complex Lie groups and their real forms. The geometric objects on which they act are of a complex analytic nature, e.g., complex manifolds or algebraic varieties. The representations are on spaces of functions which respect to the complex structure, often just vector spaces of special holomorphic or algebraic functions. A typical goal is to attempt to understand attributes of the function algebra in terms of the group structure and its action. In many aspects of the project the information of interest comes from restricting a given action of a complex reductive group to a complex subgroup or a given real form. In that setting algebraic techniques as well as geometric methods of Hamiltonian actions are applied in order to identify special regions of geometric relevance and study its representation theoretic consequences. This is often an orbit of a reductive or parabolic subgroup or of a real form of a given action of a semisimple group on an almost homogeneous manifold.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory
• Participating Person: Professorin Dr. Stéphanie Cupit-Foutou