Oberwolfach Seminars

Infinite Dimensional Kähler Manifolds

Editors: Huckleberry, Alan, Wurzbacher, Tilmann (Eds.)

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About this book

Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Introduction to Group Actions in Symplectic and Complex Geometry

    Huckleberry, Alan

    Pages 1-129

  • Infinite-dimensional Groups and their Representations

    Neeb, Karl-Hermann

    Pages 131-178

  • Borel-Weil Theory for Loop Groups

    Neeb, Karl-Hermann

    Pages 179-229

  • Coadjoint Representation of Virasoro-type Lie Algebras and Differential Operators on ensor-densities

    Ovsienko, Valentin Yu.

    Pages 231-255

  • From Group Actions to Determinant Bundles Using (Heat-kernel) Renormalization Techniques

    Paycha, Sylvie

    Pages 257-285

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-0348-8227-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA in USD
  • ISBN 978-3-7643-6602-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Infinite Dimensional Kähler Manifolds
Editors
  • Alan Huckleberry
  • Tilmann Wurzbacher
Series Title
Oberwolfach Seminars
Series Volume
31
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8227-9
DOI
10.1007/978-3-0348-8227-9
Softcover ISBN
978-3-7643-6602-5
Series ISSN
1661-237X
Edition Number
1
Number of Pages
XIII, 375
Topics