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.

Dedication.
- Acknowledgments.
- Introduction.

- Part I: Introduction to Flag Domain Theory.
- Overview.
- Structure of Complex Flag Manifolds.
- Real Group Orbits.
- Orbit Structure for Hermitian Symmetric Spaces.
- Open Orbits.
- The Cycle Space of a Flag Domain.

- Part II: Cycle Spaces as Universal Domains.
- Overview.
- Universal Domains.
- B-Invariant Hypersurfaces in Mz.
- Orbit Duality via Momentum Geometry.
- Schubert Slices in the Context of Duality.
- Analysis of the Boundary of U.
- Invariant Kobayashi Hyperbolic Stein Domains.
- Cycle Spaces of Lower-Dimensional Orbits.
- Examples.

- Part III: Analytic and Geometric Concequences.
- Overview.
- The Double Fibration Transform.
- Variation of Hodge Structure.
- Cycles in the K3 Period Domain.

- Part IV: The Full Cycle Space.
- Overview.
- Combinatorics of Normal Bundles of Base Cycles.
- Methods for Computing H1(C;O(E((q+0q)s

This monograph, divided into four parts, presents a comprehensive treatment 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, and their applications to harmonic analysis and algebraic geometry.
Key features:
- All the necessary background material is provided for the nonspecialist, thus making the book accessible to readers from a wide range of fields.
- The exposition, driven by numerous examples, is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also comes from real and complex algebraic groups and their representations as well as other areas of geometry.
- Many new results presented for the first time
- Comparisons with classical Barlet cycle spaces are given
- Good bibliography and index
Researchers and graduate students in complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, differential geometry and areas of global geometric analysis will benefit from this work.