Finite Dimensional Algebras and Related Topics

392 Pages·1994·12.416 MB·English

by  Michel Broué (auth.), Vlastimil Dlab, Leonard L. Scott (eds.)

Finite Dimensional Algebras and Related Topics
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Series C: Mathematical and Physical Sciences -Vol. 424
Finite Dimensional Algebras
and Related Topics
edited by
V. Dlab
Department of Mathematics and Statistics,
Carleton University,
Ottawa, Canada
and
L. L. Scott
Department of Mathematics,
University of Virginia,
Charlottesville, Virginia, U.S.A.
llru1ll
''
Springer-Science+Business Media, B.V.
Proceedings of the NATO Advanced Research Workshop on
Representations of Algebras and Related Topics
Ottawa, Canada
August 1G -18, 1992
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://extras.springer.com
ISBN 978-90-481-4377-1 ISBN 978-94-017-1556-0 (eBook)
DOI 10.1007/978-94-017-1556-0
Printed on acid-free paper
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© 1994 Springer Science+ Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1994
Softcover reprint of the hardcover 1st edition 1994
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
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TABLE OF CONTENTS
Preface vii
List of Participants ix
M. Broue: Equivalences of Blocks of Group Algebras
C. W. Curtis: On the Endomorphism Algebras of Gelfand-Graev Representations 27
R. Dipper: Harish-Chandra Vertices, Green Correspondence in Heeke Algebras,
and Steinbergs Tensor Product Theorem in Nondescribing Characteristic 37
S. Donkin: On Tilting Modules and Invariants for Algebraic Groups 59
Yu. A. Drozd, V. M. Futorny and S. A. Ov!iienko: Harish-Chandra Subalgebras and
Gelfand-Zetlin Modules 79
M. J. Dyer: Algebras Associated to Bruhat Intervals and Polyhedral Cones 95
K. Erdmann: Symmetric Groups and Quasi-hereditary Algebras 123
D. Happel, I. Reiten and S. 0. Smal¢: Quasitilted Algebras 163
B. Keller: Tilting Theory and Differential Graded Algebras 183
H. Lenzing: Wild Canonical Algebras and Rings of Automorphic Forms 191
B. Parshall: The Ext Algebra of a Highest Weight Category 213
J. A. de Ia Peiia: Coxeter Transformations and the Representation Theory of
Algebras 223
J. Rickard: Translation Functors and Equivalences of Derived Categories for
Blocks of Algebraic Groups 255
K. W. Roggenkamp: Blocks with Cyclic Defect (Green Orders) 265
A. N. Rudakov: Rigid and Exceptional Sheaves on a Delpezzo Surface 277
L. L. Scott: Quasihereditary algebras and Kahzdan-Lusztig theory 293
A. Skowronski: Cycles in Module Categories 309
M. Auslander and (Z). Solberg: Relative Homology 347
T. Wakamatsu: Tilting Theory and Selfinjective Algebras 361
v
PREFACE
These Proceedings report on a number of lecture series delivered at the 1992 Annual Canadian
Mathematical Seminar/ NATO Advanced Research Workshop held at Carleton University, Ottawa,
Canada during August 10-18, 1992.
The Workshop was dedicated to the interaction of finite dimensional algebras with other areas
of Mathematics, especially Lie theory, but including also algebraic geometry, automorphic forms,
finite group representation theory and mathematical physics. The Scientific Organizing Committee
consisted of M. Auslander, R. Bautista, C.W. Curtis, V. Dlab (Chairman), I.M. Gelfand, D. Han
delman, G.O. Michler, L.L. Scott and H. Tachikawa. The intellectual predecessor of this conference
was perhaps the Ottawa- Moosonee Conference organized by one of the Editors in August 1987.
That conference included similar topics on a smaller scale, and some of the activity at this Workshop
can be directly traced back to it. Nevertheless, while the serious interaction of finite dimensional
algebras with many of these other areas was somewhat novel at the Ottawa-Moosonee Conference,
it was clear at the present meeting that it has become an established feature of the mathematical
landscape, both within finite dimensional algebras and without. This volume stands as a partial
testimony to this new and welcome development.
The program of the Seminar /Workshop consisted of 27 lecture series, all listed separately in this
volume. The Editors invited a number of the lecturers to submit articles for these Proceedings, with
a preference to those lectures illustrating the interaction described above. It was expected that all
submissions would be refereed a<; appropriate; in fact, most referees reported with enthusiasm. \Ve
would like to express our gratitude to the authors who submitted contributions, and to all referees
for their assistance.
\Ve wish to express our thanks for financial support to both the Natural Sciences and En
gineering Research Council of Canada and the Scientific Division of the North Atlantic Treaty
Organization. We also wish to extend our gratitude to Drs. Istvan Agoston and Erzsebct Lukacs
for their much appreciated secretarial support and efficiency; without their generous assistance the
\Vorkshop could not have run so smoothly.
Ottawa and Charlottesville, August 1993 Vlastimil Dla.b and Leonard Scott
vii
LIST OF PARTICIPANTS
Agoston, Istvan, Mathematical Institute, Realtanoda u. 13-15, Budapest 1053, Hungary.
E~mail: [email protected]
Alperin, Jonathan L., University of Chicago, 5734 University Avenue, Chicago IL 60637, USA.
E~mail: [email protected]
Anh, Pham Ngoc, Mathematical Institute, Realtanoda u. 13~15, Budapest 1053, Hungary.
E~mail: h [email protected]
Asashiba, Hideto, Osaka City University, 3~3~138 Sugimoto, Sumiyoshi~ku, Osaka 558, Japan.
E~mail: [email protected]
Assem, Ibrahim, Universite de Sherbrooke, Sherbrooke Quebec J1K 2R1, Canada.
E~mail: iassem@udesvm. vm1.si. usherb.ca
Auslander, Maurice, Brandeis University, Waltham MA 02254, USA.
E~mail: [email protected]
Baccella, Giuseppe, Universita dell' Aquila, L'Aquila 67100, Italy.
E~mail: [email protected]
Bautista, Raymundo, Inst.itut.o de Matematicas, U.N.A.M., Circuito Exterior, Ciudad Universi~
taria, Mexico, D.F. C.P. 04510, Mexico.
E~mail: [email protected]
Bavula, V.V., Kiev University, Vladimirskaya Str. 64, Kiev 252617, Ukraine.
Dolaiios Evia, Gilda R., lnstituto Literario, #100 otte. Toluca, Edo de Mexico, Mexico.
Bondar, James, Carleton University, Ottawa Ontario KIS 5B6, Canada.
Brenner, Sheila, University of Liverpool, P.O.Box 147, Liverpool L69 3BX, Great Britain.
E~mail: [email protected]
Brodeur, Daniel, Universite de Sherbrooke, Sherbrooke Quebec J1K 2R1, Canada.
E~mail: [email protected]
Brmu'i, Michel, Ecole Nonnale Superieure, 45 rue d'Ulm, Paris 75005, France.
E~mail: [email protected]
Butler, Michael C.R., University of Liverpool, P.O.Box 147, Liverpool L69 3BX, Great Britain.
E~mail: [email protected]
Chen, Liang, University of Alberta, Edmonton Alberta T6G 2G1, Canada.
Cliff, Gerald, University of Alberta, Edmonton Alberta T6G 2G1, Canada.
E~mail: [email protected] t.h. ualberta.ca
Coelho, Flavio Ulhoa, Universidade de Sao Paulo, Caixa Postal 20.570 (ag. Iguatemi), Sao Paulo
01498~970, Brazil.
E~mail: [email protected]
Crawley~Boevey, William W., Oxford University, 24~29 St. Giles, Oxford OX1 3LB, Great
Britain.
E~mail: [email protected] .uk
Curtis, Chal'ies W., University of Oregon, Eugene OR 97403, USA.
E~mail: [email protected]
Cylke, Andrew A., Kiev University, Vladimirskaja Str. 64, Kiev 252617, Ukraine.
E~mail: [email protected]
ix
X
Dean, Andrew P., Bishop's University, Lennoxville Quebec J1M 1Z7, Canada.
Dipper, Richard, Universitat Stuttgart, Pfaffenwaldring 57, Stuttgart 80 W-7000, Germany.
E-mail: rdipp er@t unix.mathematik .uni-st u tt gart .de
Dlab, Vlastimil, Carleton University, Ottawa Ontario KlS 5B6, Canada.
E-mail: [email protected]
Donkin, Stephen, University of London, Mile End Road, London El 4NS, Great Britain.
E-mail: s.dOLlkin@qmw .ac.uk
Doty, Stephen R., Loyola University Chicago, Lake Shore Campus, Chicago IL 60626, USA.
E-mail: [email protected]
Dowbor, Piotr, Nicholas Copernicus University, Ul. Chopina 12/18, Toruli. 87-100, Poland.
E-mail: [email protected]
Draxler, Peter, Universitat Bielefeld, Bielefeld 1 W-4800, Germany.
E-mail: [email protected]
Drozd, Yuri A., Kiev University, Vladimirskaya Str. 64, Kiev 252617, Ukraine.
Du, Jie, University of New South Wales, P.O.Boxl, Kensington N.S.W. 2033, Australia.
E-mail: [email protected] .edu.au
Dyer, Matthew, University of Notre Dame, Notre Dame IN 46556, USA.
E-mail: Matthew .J .Dyer [email protected]
Erdmann, Karin, Sommerville College, Oxford OX2 6HS, Great Britain.
E-mail: [email protected]
Farahat, H.K., University of Calgary, Calgary Alberta T2N 1N4, Canada.
Futorny, Viatcheslav M., Queen's University, Kingston Ontario K7L 3N6, Canada.
E-mail: [email protected]
Geiss, Christo£, Universitiit Bayreuth, Postfach 101251, W-86580 Bayreuth, Germany.
E-mail: [email protected]
Gentle, Ron, Eastern Washington University, Cheney WA 99004, USA.
Glazman Nowalski, Mary, Faculdad de Ciencias, U.N.A.M., Circuito Exterior, Ciudad Univer
sitaria, Mexico, D.F. C.P. 04510, Mexico.
Guo, Jin Yun, Hunan Normal University, Changsha Hunan 410006, China.
Handelman, David, University of Ottawa, 585 King Edward, Ottawa Ontario KIN 9B4, Canada.
E-mail: dehsg@acad vml.uottawa.ca
Happel, Dieter, Technische Universitiit Chemnitz, Postfach 964, 0-9010 Chemnitz, Germany.
E-mail: [email protected]
Heath, Peter, Carleton University, Ottawa Ontario K1S 5B6, Canada.
E-mail: [email protected]
Hille, Lutz, Universitiit Bielefeld, Bielefeld 1 W-4800, Germany.
E-mail: [email protected]
Hoffman, Peter N., University of Waterloo, Waterloo Ontario N2L 3G1, Canada.
von Hohne, Hans-Joachim, Freie Universitiit Berlin, Arnimallee 3, Berlin 33 D-1000, Germany.
Iwanaga, Yasuo, Shinshu University, Nishi-Nagano 6, Nagano 380, Japan.
E-mail: [email protected]
Kasjan, S., Nicholas Copernicus University, Ul. Chopina 12/18, Toruli. 87-100, Poland.
E-mail: kasjan@ ma.Uorun.edu.pl
XI
Keller, Bernhard, Univcrsite Paris 7, 2, pl. Jussieu, Paris Cedex 05 F-75251, France.
E-mail: keller@mathp7 .jussieu.fr
Kerner, Otto, Heinrich Heine Universitiit Dusseldorf, Universitatstr. 1, Dusseldorf 1 W-4000,
Germany.
E-mail: [email protected]
Konig, Steffen, Universitiit Bielefeld, Bielefeld 1 W-4800, Germany.
E-mail: [email protected]
Koshitani, Shigeo, Chiba University, 1-33 Yayoi-cho, Chiba-city 260, Japan.
E-mail: [email protected]
Krause, Henning, Universitat Bielefeld, Bielefeld 1 W-4800, Germany.
E-mail: [email protected]
Larri6n, Francisco, Instit.uto de Matematicas, U.N.A.M., Circuito Exterior, Ciudad Universitaria,
Mexico, D.F. C.P. 04510, Mexico.
E-mail: [email protected]
Lenzing, Helmut, Universitiit Paderborn, Warburgerstr. 100, Paderborn W-4790, Germany.
E-mail: [email protected]
Lukacs, Erzsebet, Technical University, Miiegyetem rkp. 9, Budapest H-1111, Hungary.
E-mail: [email protected]
MacKenzie, Kenneth W., University of Liverpool, P.O.Box 147, Liverpool L69 3BX, Great
Britain.
E-mail: [email protected]
Malliavin, Marie-Paule, Universite Pierre et Marie Curie, 4, place Jussieu, Paris Cedex 02 75252,
France.
Marko, Frantisek, Carleton University, Ottawa, Ontario K1Y 5B6, Canada.
E-mail: [email protected]
Marmaridis, Nikolaos, University of loannina, loannina 45110, Greece.
E-mail: [email protected]
Martinez-Villa, Roberto, Instituto de Matematicas, U .N.A.M., Circuito Exterior, Ciudad Uni
versitaria, Mexico, D.F. C.P. 04510, :Mexico.
E-mail: imate@unamvm 1. bitnet
Masaike, Kanzo, Tokyo Gakugei University, Koganei, Tokyo 184, Japan.
E-mail: masaike@clezio. u-gakugei.ac .jp
May S.J., Michael, 12 Linnaean St., Cambridge MA 02138, USA.
E-mail: [email protected]
McKay, John, Concordia University, Montreal Quebec H3G 1M8, Canada.
E-mail: [email protected]
Meltzer, Hagen, Universitat Paderborn, Warburgerstr. 100, Paderborn W-4790, Germany.
E-mail: [email protected]
Merklen, Hector, Universidade de Sao Paulo, Caixa Postal 20.570 (ag. lguatemi), Sao Paulo
01498, Brazil.
E-mail: [email protected]
Moody, Robert V., Universit.y of Alberta, EJmonton Alberta T6G 2G1, Canada.
E-mail: userrvmo@mts. ucs .ualberta.ca
Neher, Erhard, University of Ottawa, 585 King Edward, Ottawa Ontario KIN 984, Canada.
E-n1ail: neher(Q!acad vn1l. uottawa.ca
Nguyen, Du. Harvard l:niversity, Cambridge 1\IA 02138, USA.