Representation Theories and Algebraic Geometry

454 Pages·1998·9.684 MB·English

by  Michel Brion (auth.), Abraham Broer, A. Daigneault, Gert Sabidussi (eds.)

Representation Theories
and Aigebraic Geometry
NATO ASI Series
Advanced Science Institute Series
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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