On the automorphism groups of complex homogeneous spaces
Representation Theory
2008-02-03 v1
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.
Cite
@article{arxiv.math/9506218,
title = {On the automorphism groups of complex homogeneous spaces},
author = {Edward G. Dunne and Roger Zierau},
journal= {arXiv preprint arXiv:math/9506218},
year = {2008}
}