Advances in Geometry

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

• ISBN13: 9780817640446
• ISBN10: 0817640444
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Springer Verlag

Summary

This collection of invited mathematical papers by an impressive list of distinguished mathematicians is an outgrowth of the scientific activities at the Center for Geometry and Mathematical Physics of Penn State University.The articles present new results or discuss interesting perspectives on recent work that will be of interest to researchers and graduate students working in symplectic geometry and geometric quantization, deformation quantization, non-commutative geometry and index theory, quantum groups, holomorphic algebraic geometry and moduli spaces, quantum cohomology, algebraic groups and invariant theory, and characteristic classes. Contributors to the volume:A. Astashkevich, A. Banyaga, P. Bieliavsky, A. Broer, J.-L. Brylinski, R. Brylinski, S. Fomin, P. Foth, P. Gajer, M. Kapovich, A.A. Kirillov, E. Meinrenken, J. Millson, G. Nagy, R. Nest, A. Postnikov, J.-E. Roos, B. Tsygan, N. Wallach, C. Woodward

Table of Contents

Preface	vii
On Karabegov's Quantizations of Semisimple Coadjoint Orbits	1	(18)
Alexander Astashkevich
Exotic Differential Operators on Complex Minimal Nilpotent Orbits	19	(34)
Alexander Astashkevich
Ranee Brylinski
The Geometry Surrounding the Arnold-Liouville Theorem	53	(18)
Augustin Banyaga
Symmetric Spaces and Star Representations	71	(12)
Pierre Bieliavsky
Hyperplane Arrangements, Springer Representations and Exponents	83	(12)
Abraham Broer
Comparison of the Beilinson-Chern Classes with the Chern-Cheeger-Simons Classes	95	(12)
Jean-Luc Brylinski
Geometric Construction of Quillen Line Bundles	107	(40)
Jean-Luc Brylinski
Quadratic Algebras, Dunkl Elements, and Schubert Calculus	147	(36)
Sergey Fomin
Anatol N. Kirillov
Logarithmic Forms with Twisted Coefficients	183	(12)
Philip A. Foth
Higher Holonomies, Geometric Loop Groups and Smooth Deligne Cohomology	195	(42)
Pawel Gajer
Moduli Spaces of Linkages and Arrangements	237	(34)
Michael Kapovich
John J. Millson
Moduli Spaces of Flat Connections on 2-Manifolds, Cobordism, and Witten's Volume Formulas	271	(26)
E. Meinrenken
C. Woodward
A Rigidity Property for Quantum SU(3) Groups	297	(40)
Gabriel Nagy
On the Cohomology Ring of an Algebra	337	(34)
Ryszard Nest
Boris Tsygan
On A Quantum Version of Pieri's Formula	371	(14)
Alexander Postnikov
Some Non-Koszul Algebras	385	(6)
Jan-Erik Roos
A Variety of Solutions to the Yang-Baxter Equation	391
Nolan R. Wallach