Cycle Spaces of Flag Domains

Presents a state-of-the art and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Driven by numerous examples, the exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and...
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Presents a state-of-the art and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Driven by numerous examples, the exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry. All the necessary background material is provided for the nonspecialist, including a good bibliography and index, thus making the book accessible to readers from a wide range of fields. Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.