Cycle spaces associated to group actions

Alan Huckleberry

Bochum, Germany

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Abstract

If G₀ is a real form of a complex semisimple group G, then the G₀-orbits in G-homogeneous rational manifolds provide complex geometric contexts for realization of its representations. Conversely, such orbits and the related representation theory often arise in questions of complex analysis, e.g., concerning moduli of complex varieties. In most cases these orbits possess a certain degree of pseudoconcavity, and, in order to shift from the level of cohomology to that of function spaces, one considers associated cycle spaces. Our recent work (joint with J.A. Wolf and with G. Fels) which gives an explicit description of these cycle spaces will be explained in the talk.