EAN: 9783322802699

LIE GROUP ACTIONS IN COMPLEX ANALYSIS - DIMITRI...

This book was planned as an introduction to a vast area  where many contri butions have been
made in recent years. The choice of material is based on my understanding of the role of Lie
groups in complex analysis. On the one hand  they appear as the automorphism groups of certain
complex spaces  e. g.   bounded domains in en or compact spaces  and are therefore important as
being one of their invariants. On the other hand  complex Lie groups and  more generally 
homoge neous complex manifolds  serve as a proving ground  where it is often possible to
accomplish a task and get an explicit answer. One good example of this kind is the theory of
homogeneous vector bundles over flag manifolds. Another example is the way the global analytic
properties of homogeneous manifolds are translated into algebraic language. It is my pleasant
duty to thank A. L. Onishchik  who first introduced me to the theory of Lie groups more than 25
years ago. I am greatly indebted to him and to E. B. Vinberg forthe help and advice they have
given me for years. I would like to express my gratitude to M. Brion  B. GilIigan  P. Heinzner
A. Hu kleberry  and E. Oeljeklaus for valuable discussions of various subjects treated here. A
part of this book was written during my stay at the Ruhr-Universitat Bochum in 1993. I thank
the Deutsche Forschungsgemeinschaft for its research support and the colleagues in Bochum for
their hospitality.

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