Lie Theory and Geometry In Honor of Bertram Kostant
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these area
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Series Editors J. Oesterle A. Weinstein
Lie Theory and Geometry In Honor of Bertram Kostant Jean-Luc Brylinski Ranee Brylinski Victor Guillemin Victor Kac 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 Guillemin Department of Mathematics MIT Cambridge, M A 02139
Victor Kac Department of Mathematics MIT Cambridge, M A 02139
Library of Congress Cataloging In-Publication Data Lie theory and geometry : in honor of Bertram Kostant / Jean-Luc Brylinski... [et al.], editors. p. cm. - (Progress in mathematics ; v. 123) Invited papers, some originated at a symposium held at MIT in May 1993. Includes bibliographical references. ISBN 978-1-4612-6685-3 ISBN 978-1-4612-0261-5 (eBook) DOI 10.1007/978-1-4612-0261-5 1. Lie groups. 2. Geometry. I. Kostant, Bertram. II. Brylinski, J.-L. (Jean-Luc) III. Series: Progress in mathematics : vol. 123. QA387.L54 1994 94-32297 512'55~dc20 CIP Printed on acid-free paper © Springer Science+Business Media New York 1994 Originally published by Birkhäuser Boston in 1994 Softcover reprint of the hardcover 1st edition 1994 Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Springer Science+Business Media, LLC, for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed directly to Springer Science+Business Media, LLC.
ISBN 978-1-4612-6685-3 Text prepared by TeXniques, Inc. from disks.
987654321
Bertram Kostant
Table of Contents
Preface
. . . . . ix
Normality of Some Nilpotent Varieties and Cohomology of Line Bundles on the Cotangent Bundle of the Flag Variety Bram Broer
1
Holomorphic Quantization and Unitary Representations of the Teichmiiller Group Jean-Luc Brylinski and Dennis McLaughlin . . . . . . . . . . . 21 Differential Operators on Conical Lagrangian Manifolds Ranee Brylinski and Bertram Kostant . . . . . . . . . . . . . . 65 Groups and the Buckyball Fan R. K. Chung, Bertram Kostant, and Shlomo Sternberg . . . . . 97 Spinor and Oscillator Representations of Quantum Groups Jintai Ding and Igor B. Frenkel. . . . . . . . . . .
127
Familles coherentes sur les groupes de Lie semi-simples et restriction aux sous-groupes compacts maximaux Michel Duflo and Michele Vergne . . . . . . . . .
167
The Differential Geometry of Fedosov's Quantization Claudio Emmrich and Alan Weinstein . . . .
217
Closedness of Star Products and Cohomologies Moshe Flato
