Advances in Geometry
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
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Series Editors Hyman Bass Joseph Oesterle Alan Weinstein
Advances in Geometry Jean-Luc Brylinski Ranee Brylinski Victor Nistor Boris Tsygan Ping Xu Editors
Springer Science+Business Media, LLC
Jean-Luc Brylinski Department of Mathematics Penn State University University Park, PA 16802
Ranee Brylinski Department of Mathematics Penn State University University Park, PA 16802
Victor Nistor Department of Mathematics Penn State University University Park, PA 16802
Boris Tsygan Department of Mathematics Penn State University University Park, PA 16802
PingXu Department of Mathematics Penn State University University Park, PA 16802 Library of Congress Cataloging-in-PubUcation Data Advances in geometry / Jean-Luc Brylinski ... [et aL]. p. cm. -- (Progress in mathematics ; 172) Includes bibliographical references. ISBN 978-1-4612-7274-8 ISBN 978-1-4612-1770-1 (eBook) DOI 10.1007/978-1-4612-1770-1
1. Geometry. 1. Brylinski, J.-L. (Jean-Luc) Progress in mathematics (Boston, Mass.) ; 172. QA446.A28 1998 516--dc21
II. Series: 98-43464 CIP
AM8 8ubject Classifications: Primary--05El5, 14812, 14C40, 14F05, 14F25, 14F35, 14Fxx, 14J99, 141.30, 14M15,14NI0, 16E40, 16E99, 16832, 17837, 17870, 18G15, 52830, 53C, 53C12, 53C15, 53C35, 53C05,55P35,55R40,57M25,51T35,58F06,58AI4,58830,81R50,81810, 70" Secondary--14M15,14P05,20F36 Printed on acid·free paper.
© 1999 Springer Science+8usiness Media New York Origioally published by Birkhl1user Boston in 1999 Softcover reprint of the hardcover 1st edition 1999 Ali rights reserved. This work may not be translated ar copied in whole ar in part without the written permission of the publisher Springer Science+Business Media, LLC . except for brief excerpts in connection with reviews ar scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known ar hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not ta be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may according1y be used freely by anyone. ISBN 978-1-4612-7274-8 Reformatted in IA1EX by TEXniques, Inc., Cambridge, MA
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CONTENTS
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. vii On Karabegov's Quantizations of Semisimple Coadjoint Orbits Alexander Astashkevich ... ......................................... 1 Exotic Differential Operators on Complex Minimal Nilpotent Orbits Alexander Astashkevich and Ranee Brylinski ..... ................. 19 The Geometry Surrounding the Arnold-Liouville Theorem Augustin Banyaga ................................................ 53 Symmetric Spaces and Star Representations Pierre Bieliavsky. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71 Hyperplane Arrangements, Springer Re
