© 1999

Advances in Geometry

  • Jean-Luc Brylinski
  • Ranee Brylinski
  • Victor Nistor
  • Boris Tsygan
  • Ping Xu

Part of the Progress in Mathematics book series (PM, volume 172)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Alexander Astashkevich, Ranee Brylinski
    Pages 19-51
  3. Pierre Bieliavsky
    Pages 71-82
  4. Jean-Luc Brylinski
    Pages 107-146
  5. Sergey Fomin, Anatol N. Kirillov
    Pages 147-182
  6. Philip A. Foth
    Pages 183-193
  7. Michael Kapovich, John J. Millson
    Pages 237-270
  8. Ryzard Nest, Boris Tsygan
    Pages 337-370
  9. Alexander Postnikov
    Pages 371-383
  10. Jan-Erik Roos
    Pages 385-389
  11. Back Matter
    Pages 401-403

About this book


This book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998. The Center was created in the Mathematics Department at Penn State in the fall of 1996 for the purpose of promoting and supporting the activities of researchers and students in and around geometry and physics at the university. The CGMP brings many visitors to Penn State and has ties with other research groups; it organizes weekly seminars as well as annual workshops The book contains 17 contributed articles on current research topics in a variety of fields: symplectic geometry, quantization, quantum groups, algebraic geometry, algebraic groups and invariant theory, and character­ istic classes. Most of the 20 authors have talked at Penn State about their research. Their articles present new results or discuss interesting perspec­ tives on recent work. All the articles have been refereed in the regular fashion of excellent scientific journals. Symplectic geometry, quantization and quantum groups is one main theme of the book. Several authors study deformation quantization. As­ tashkevich generalizes Karabegov's deformation quantization of Kahler manifolds to symplectic manifolds admitting two transverse polarizations, and studies the moment map in the case of semisimple coadjoint orbits. Bieliavsky constructs an explicit star-product on holonomy reducible sym­ metric coadjoint orbits of a simple Lie group, and he shows how to con­ struct a star-representation which has interesting holomorphic properties.


Algebra Invariant Mathematics Operator calculus equation geometry linear optimization manifold symplectic geometry theorem

Editors and affiliations

  • Jean-Luc Brylinski
    • 1
  • Ranee Brylinski
    • 1
  • Victor Nistor
    • 1
  • Boris Tsygan
    • 1
  • Ping Xu
    • 1
  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA

Bibliographic information

  • Book Title Advances in Geometry
  • Authors Jean-Luc Brylinski
    Ranee Brylinski
    Victor Nistor
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Boston 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4044-6
  • Softcover ISBN 978-1-4612-7274-8
  • eBook ISBN 978-1-4612-1770-1
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XI, 403
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Mathematical Methods in Physics
    Applications of Mathematics
  • Buy this book on publisher's site