On the automorphism groups of complex homogeneous spaces

1995/06/12 by Edward G. Dunne, Dunne, Edward G., Roger Zierau +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/9506218

arxiv created 1995/06/12 · openalex publication_date 1995/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 G₀ of G form an interesting class of complex homogeneous spaces, which play an important role in the representation theory of G₀. 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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