Representation Theories and Algebraic Geometry PDF
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Representation Theories and Aigebraic Geometry NATO ASI Series Advanced Science Institute Series ASeries presenting the results o( activities sponsored by the NATO Science Committee, which aims at the dissemination o( advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Seien ces Plenum Publishing Corporation B Physics London and New York C Mathematlcal and Physical Sciences Kluwer Academic Publishers D Behavioural and Social Sciences Dordrecht, Boston and London E Applied Selences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global Environment Change PARTNERSHIP SUB-SERIES 1. Disarmament Technologies Kluwer Academic Publishers 2. Environment Springer-Verlag I Kluwer Academic Publishers 3. High Technology Kluwer Academic Publishers 4. Seien ce and Technology Policy Kluwer Academic Publishers 5. Computer Networking Kluwer Academic Publishers The Partnership Sub-Series incorporates activities undertaken in collaboration with NATO's Cooperation Partners, the countries o( the CIS and Central and Eastern Europe, in Priority Areas o( concern to those countries. NATO-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords andlor abstracts) to about 50,000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATQ-PCQ-DATA BASE is possible via a CD-ROM "NATO Science and Technology Disk" with user-friendly retrieval software in English, French, and German (©WTV GmbH and DATAWARE Technologies, Inc. 1989). The CD-ROM contains the AGARD Aerospace Data base. The CD-ROM can be ordered through any member of the Board of Publishers or through NATQ-PCO, Overijse, Belgium. Series C: Mathematical and Physical Sciences - Vol. 514 Representation Theories and Aigebraic Geometry edited by A. Broer and A. Daigneault University of Montreal, Department of Mathematics and Statistics, Montreal, Canada Technical Editor Gert Sabidussi University of Montreal, Department of Mathematics and Statistics, Montreal, Canada Springer-Science+Business Media, B.V. Proceedings of the NATO Advanced Study Institute on Representation Theories and Aigebraic Geometry Montreal, Canada July 28 -August 8, 1997 A C.I.P. Catalogue record for this book is available from the Library of Congress. Additional material to this book can be downloaded from http://extra.springer.com. ISBN 978-90-481-5075-5 ISBN 978-94-015-9131-7 (eBook) DOI 10.1007/978-94-015-9131-7 Printed an acid-free paper AII Rights Reserved © 1998 Springer Science+Business Media Dordrecht Originally published byKluwer Academic Publishers in 1998 Softcover reprint of the hardcover lst edition 1998 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo copying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Table of Contents Preface vii Key to group pieture xi Participants xiii Contributors xxi Michel BRION Equivariant cohomology and equivariant intersection theory 1 Abraham BROER Lectures on decomposition classes 39 Ranee BRYLINSKI Instantons and Kähler geometry of nilpotent orbits 85 Vietor GINZBURG Geometrie methods in the representation theory of Hecke algebras and quantum groups 127 Jens Carsten JANTZEN Representations of Lie algebras in prime characteristie 185 Anthony JOSEPH Sur l'annulateur d'un module de Verma 237 Friedrieh KNOP Some remarks on multiplicity free spaces 301 Venkatramani LAKSHMIBAI, Peter LITTELMANN and Peter MAGYAR Standard Monomial Theory and applications 319 George LUSZTIG Canonieal bases and Hall algebras 365 Wolfgang SOERGEL Combinatories of Harish-Chandra modules 401 Tonny A. SPRINGER Schubert varieties and generalizations 413 Index 441 Preface This volume contains the Proceedings of the 36th session of the Seminaire de MatMmatiques Superieures held July 28 - August 8, 1997 at the Universite de Montreal. This session was a NATO Advanced Study Institute. The topic was Representation Theories and Algebraic Geometry, dealing with the intensive interaction between various representation theories and algebraic geometry. This interaction is responsable for much of the enormous progress we have seen during the last two decades in representation theory. Twelve speakers presented mini-courses of four to five hours each. The speakers were Michel Brion, Bram Broer, Ranee Brylinski, Victor Ginzburg, Jens Jantzen, Tony Joseph, Friedrich Knop, Peter Littelmann, George Lusztig, Dale Peterson, Wolfgang Soergel and Tonny Springer. We thank them for the high quality of the content and the stimulating presentation of their lectures. Accounts of eleven of these courses are included in this volume. The Advanced Study Institute was attended by 76 participants from 12 countries. We thank them for their lively interest and for providing for a very pleasant audience. The infor mal discussions were very friendly and intensive, leading more than once to new cooperations and joint work. Our thanks go to Aubert Daigneault and Ghislaine David who took care of the organi sational side of the Advanced Study Institute with traditional smoothness. We thank Gert Sabidussi and Josee Desharnais for preparing the publication of these Proceedings. Finally, we would like to express our gratitude to NATO for its support of this meeting through its Advanced Study Institute programme; also to the Universite de Montreal for additional funding. Special thanks go to Dr. Luis Veiga da Cunha of the Scientific and Environmental Affairs Division of NATO for his help and kind counsel in connection with this ASI. The Editor vii Key to group picture 1 P. Magyar 44 D. Shmelkin 2 V. Mazorchuk 45 K. Günzl 3 A. Astashkevich 46 R. Bedard 4 V. Baranovsky 47 P. Trapa 5 J. Carrell 48 E. Sommers 6 A.Okounov 49 R. W. Donley 7 E. Tevelev 50 M. Nevins 8 51 K. Rietsch 9 O. Rossi-Doria 52 W. Kraskiewicz 10 N. Handzy 53 M. Shimozono 11 R. De Man 54 M. Gorelik 12 W. Graham 55 A. Rittatore 13 1. Gordon 56 E. Vasserot 14 J. Weyman 57 J.-L. Brylinski 15 D. Wehlau 58 F. Sottile 16 F. Ziegler 59 W. Haboush 17 S. Ryom-Hansen 60 D. Snow 18 D. Woodcock 61 J. G. Jensen 19 G. Röhrle 62 20 R. Marsh 63 J. Beck 21 C. Cunningham 64 G. Sabidussi 22 1. Kedim 65 A. Daigneault 23 J. Winkelmann 66 J. Morand 24 J. Paradowski 67 Y. Sanderson 25 F. Vaccarino 68 D.-N. Verma 26 J. E. Humphreys 69 C. Kriloff 27 C. Pillen 70 N. Cantarini 28 M. Thoma 71 F. Knop 29 S. Agnihotri 72 V. Lakshmibai 30 P.-L. Montagard 73 R. Ushirobira 31 J. F. Thomsen 74 P. Littelmann 32 M.-A. Levasseur 75 M. Varagnolo 33 G. Green 76 R. Dehy 34 Y. Papageorgiou 77 A. Berenstein 35 M. Härterich 78 G. David 36 D. Timashev 79 R. Brylinski 37 G. Letzter 80 V. Ginzburg 38 O. Garotta 81 W. Soergel 39 R. Taillefer 82 J. C. Jantzen 40 S. Cupit 83 A. Joseph 41 1. Musson 84 A. Broer 42 R. Yu 85 T. A. Springer 43 P. Foth 86 M. Brion xi Participants Sharad AGNIHOTRI Arkady BERENSTEIN Department of Mathematics/Cl200 Department of Mathematics University of Texas, TX 78712-1082 White Hall, Cornell University USA Ithaca, NY 14853-7901 [email protected] USA [email protected] Alexander ASTASHKEVICH Department of Mathematics Jean-Luc BRYLINSKI University of California, Davis Department of Mathematics Davis, CA 95616-8633 218 McAllister Bldg. USA Pennsylvania State University [email protected] University Park, PA 16802-6401 USA [email protected] Ali BAKLOUTI Departement de mathematiques Universite de Metz, lIe de Saulcy Nicoletta CANTARINI F-57045 Metz Cedex 01 Dipartimento di Matematica France Universita di Pisa [email protected] Via F. Buonarroti 2 1-56127 Pisa Italy Vladimir BARANOVSKY [email protected] Department of Mathematics University of Chicago 5734 S. University Ave. James CARRELL Chicago, IL 60637-1546 Department of Mathematics USA University of British Columbia [email protected] Vancouver, BC, V6T lZ4 Canada [email protected] Jonathan BECK Department of Mathematics University of Chicago Clifton CUNNINGHAM 5734 S. University Ave. Department of Mathematics Chicago-l546, IL 60637 University of Toronto USA Toronto, Ont., M5S 3G3 [email protected] Canada [email protected] Robert BEDARD Departement de mathematiques Stephanie CUPIT Universite du Quebec a Montreal Departement de Mathematiques CP 8888, Succ. Centre-ville Universite Louis Pasteur Montreal, Que., H3C 3P8 7, rue Rene Descartes Canada F-67084 Strasbourg Cedex [email protected] France [email protected] xiii
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