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, as well as their applications to harmonic analysis and algebraic geometry.

Key features:

• Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist
• Many new results presented for the first time
• 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
• Comparisons with classical Barlet cycle spaces are given
• Good bibliography and index.

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.

Written for: Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, areas of global geometric analysis

• Introduction
• Part I: Introduction to Flag Domain Theory
  • 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
  • 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
  • The Double Fibration Transform
  • Variation of Hodge Structure
  • Cycles in the K3 Period Domain
• Part IV: The Full Cycle Space
  • Combinatorics of Normal Bundles of Base Cycles
  • Methods for Computing H1(C;O(E((q+0q)s)))
  • Classification for Simple g0 with rank t < rank g
  • Classification for rank t = rank g
  • References