On the automorphism groups of complex homogeneous spaces

Edward G. Dunne; Roger Zierau

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On the automorphism groups of complex homogeneous spaces

Edward G. Dunne·Roger Zierau

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Abstract

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the representation theory of G_0. We find that the group of automorphisms, i.e., the holomorphic diffeomorphisms, is a finite-dimensional Lie group, except for a small number of open orbits, where it is infinite dimensional. In the finite-dimensional case, we determine its structure. Our results have some consequences in representation theory.

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BibTeX RIS

Edward G. Dunne, Roger Zierau. 1995-06-12. On the automorphism groups of complex homogeneous spaces. https://arxiv.org/abs/math/9506218

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