Gregor Fels, Alan T. Huckleberry, Joseph A. Wolf

Cycle Spaces of Flag Domains

A Complex Geometric Viewpoint

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Progress in Mathematics Nr.245
• Verlag: Springer, Basel
• Artikelnr. des Verlages: 11380023
• 2006
• Seitenzahl: 360
• Erscheinungstermin: 12. Dezember 2005
• Englisch
• Abmessung: 241mm x 160mm x 24mm
• Gewicht: 626g
• ISBN-13: 9780817643911
• ISBN-10: 0817643915
• Artikelnr.: 14732352

Autorenporträt

Gregor Fels, University of Tübingen, Germany / Alan Huckleberry, University of Bochum, Germany / Joseph A. Wolf, University of California, Berkeley, CA, USA

Inhaltsangabe

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

---

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.- 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.- Analytic and Geometric Consequences.- The Double Fibration Transform.- Variation of Hodge Structure.- Cycles in the K3 Period Domain.- The Full Cycle Space.- Combinatorics of Normal Bundles of Base Cycles.- Methods for Computing H1(C; O).- Classification for Simple with rank < rank .- Classification for rank = rank .

Rezensionen

From the reviews:

"Cycle spaces can be a useful tool in the study of real semisimple Lie groups, and the research monograph which is reviewed here is devoted to describing their features. The exposition ... is in principle self-contained for a good graduate reader, who will also find a wealth of concrete examples. ... the approach used by the authors throughout this monograph is based on a combination of group-theoretical methods ... the result is an intriguing melting pot, opening interesting perspectives of interaction among different research branches." (Corrado Marastoni, Mathematical Reviews, Issue 2006 h)

"A systematic exposition of the background, methods, and recent results in the theory of cycle spaces of flag domains. ... The value of this progress in mathematics volume to a wide group of researchers ... is indisputable. They all will admire the volume for the many new results presented for the first time. Your reviewer would strongly recommend that you spend a few hours with this volume long enough to familiarize yourself with its contents. You'll be back for the details when you need them." (Current Engineering Practice, Vol. 48, 2005-2006)