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Birkhäuser

Advances in Geometry

Volume 1

  • Book
  • © 1999

Overview

Editors:
  1. Jean-Luc Brylinski

    1. Department of Mathematics, Penn State University, University Park, USA

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  2. Ranee Brylinski

    1. Department of Mathematics, Penn State University, University Park, USA

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  3. Victor Nistor

    1. Department of Mathematics, Penn State University, University Park, USA

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  4. Boris Tsygan

    1. Department of Mathematics, Penn State University, University Park, USA

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  5. Ping Xu

    1. Department of Mathematics, Penn State University, University Park, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
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  2. On Karabegov’s Quantizations of Semisimple Coadjoint Orbits

    • Alexander Astashkevich
    Pages 1-18

  3. Exotic Differential Operators on Complex Minimal Nilpotent Orbits

    • Alexander Astashkevich, Ranee Brylinski
    Pages 19-51

  4. The Geometry Surrounding the Arnold-Liouville Theorem

    • Augustin Banyaga
    Pages 53-69

  5. Symmetric Spaces and Star Representations

    • Pierre Bieliavsky
    Pages 71-82

  6. Hyperplane Arrangements, Springer Representations and Exponents

    • Abraham Broer
    Pages 83-93

  7. Comparison of the Beilinson-Chern Classes With the Chern-Cheeger-Simons Classes

    • Jean-Luc Brylinski
    Pages 95-105

  8. Geometric Construction of Quillen Line Bundles

    • Jean-Luc Brylinski
    Pages 107-146

  9. Quadratic Algebras, Dunkl Elements, and Schubert Calculus

    • Sergey Fomin, Anatol N. Kirillov
    Pages 147-182

  10. Logarithmic Forms with Twisted Coefficients

    • Philip A. Foth
    Pages 183-193

  11. Higher Holonomies, Geometric Loop Groups and Smooth Deligne Cohomology

    • Pawel Gajer
    Pages 195-235

  12. Moduli Spaces of Linkages and Arrangements

    • Michael Kapovich, John J. Millson
    Pages 237-270

  13. Moduli Spaces of Flat Connections on 2-Manifolds, Cobordism, and Witten’s Volume Formulas

    • E. Meinrenken, C. Woodward
    Pages 271-295

  14. A Rigidity Property for Quantum SU(3) Groups

    • Gabriel Nagy
    Pages 297-336

  15. On the Cohomology Ring of an Algebra

    • Ryzard Nest, Boris Tsygan
    Pages 337-370

  16. On a Quantum Version of Pieri’s Formula

    • Alexander Postnikov
    Pages 371-383

  17. Some Non-Koszul Algebras

    • Jan-Erik Roos
    Pages 385-389

  18. A Variety of Solutions to the Yang-Baxter Equation

    • Nolan R. Wallach
    Pages 391-399

  19. Back Matter

    Pages 401-403
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Keywords

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.

Editors and Affiliations

  • Department of Mathematics, Penn State University, University Park, USA

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

Bibliographic Information

  • Book Title: Advances in Geometry

  • Book Subtitle: Volume 1

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

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1770-1

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1999

  • Hardcover ISBN: 978-0-8176-4044-6Published: 01 December 1998

  • Softcover ISBN: 978-1-4612-7274-8Published: 21 October 2012

  • eBook ISBN: 978-1-4612-1770-1Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XI, 403

  • Topics: Differential Geometry, Geometry, Mathematical Methods in Physics, Applications of Mathematics

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