Lie Group Actions in Complex Analysis

1. Front Matter

   Pages i-vii

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2. Introduction

   • Dmitri N. Akhiezer

   Pages 1-2

3. Lie Theory

   • Dmitri N. Akhiezer

   Pages 3-30

4. Automorphism Groups

   • Dmitri N. Akhiezer

   Pages 31-62

5. Compact Homogeneous Manifolds

   • Dmitri N. Akhiezer

   Pages 63-104

6. Homogeneous Vector Bundles

   • Dmitri N. Akhiezer

   Pages 105-134

7. Function Theory on Homogeneous Manifolds

   • Dmitri N. Akhiezer

   Pages 135-180

8. Concluding Remarks

   • Dmitri N. Akhiezer

   Pages 181-185

9. Back Matter

   Pages 186-204

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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.

• Algebra
• Automorphism groups
• Compact homogeneous manifolds
• Complex analysis
• Function theory on homogeneous manifolds
• Homogeneous vector bundles Theory

• Moskau, Russia

  Dmitri N. Akhiezer

Prof. Dr. Dimitri Akhiezer lehrt Mathematik an einer Moskauer Universität.

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