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© 2006

Cycle Spaces of Flag Domains

A Complex Geometric Viewpoint

Benefits

  • Driven by numerous examples from the complex geometric viewpoint

  • New results presented for the first time

  • Widely accessible, with all necessary background material provided for the nonspecialist

  • Comparisons with classical Barlet cycle spaces are given

  • Good bibliography and index

Book

Part of the Progress in Mathematics book series (PM, volume 245)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Introduction to Flag Domain Theory

  3. Cycle Spaces as Universal Domains

  4. Analytic and Geometric Consequences

    1. Front Matter
      Pages 203-206

About this book

Introduction

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.

Keywords

Complex analysis Representation theory differential geometry harmonic analysis manifold

Authors and affiliations

  1. 1.Fakultät für Mathematik und PhysikUniversität TübingenTübingenGermany
  2. 2.Institut für MathematikRuhr-Universität BochumBochumGermany
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

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)