Advances in Geometry

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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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

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

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

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