Progress in Mathematics
cover

Cycle Spaces of Flag Domains

A Complex Geometric Viewpoint

Authors: Fels, Gregor, Huckleberry, Alan, Wolf, Joseph A.

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About this book

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.

Reviews

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)


Table of contents (20 chapters)

Table of contents (20 chapters)
  • Structure of Complex Flag Manifolds

    Pages 5-26

  • Real Group Orbits

    Pages 27-30

  • Orbit Structure for Hermitian Symmetric Spaces

    Pages 31-36

  • Open Orbits

    Pages 37-53

  • The Cycle Space of a Flag Domain

    Pages 55-71

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-0-8176-4479-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-8176-4391-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Cycle Spaces of Flag Domains
Book Subtitle
A Complex Geometric Viewpoint
Authors
Series Title
Progress in Mathematics
Series Volume
245
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4479-6
DOI
10.1007/0-8176-4479-2
Hardcover ISBN
978-0-8176-4391-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XX, 339
Topics