Diagram Geometry Related to Classical Groups and Buildings
This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geo
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A Series of Modern Surveys in Mathematics
Editorial Board L. Ambrosio, Pisa G.-M. Greuel, Kaiserslautern M. Gromov, Bures-sur-Yvette J. Jost, Leipzig J. Kollár, Princeton S. S. Kudla, Toronto G. Laumon, Orsay H. W. Lenstra, Jr., Leiden J. Tits, Paris D. B. Zagier, Bonn Managing Editor R. Remmert, Münster
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Volume 57
Francis Buekenhout r Arjeh M. Cohen
Diagram Geometry Related to Classical Groups and Buildings
Francis Buekenhout Dépt. Mathématique Université Libre de Bruxelles Académie royale de Belgique Bruxelles, Belgium
Arjeh M. Cohen Dept. Mathematics & Computer Science Eindhoven University of Technology Eindhoven, Netherlands
ISSN 0071-1136 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISBN 978-3-642-34452-7 ISBN 978-3-642-34453-4 (eBook) DOI 10.1007/978-3-642-34453-4 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013930009 Mathematics Subject Classification: 51E24, 51Axx, 20Bxx, 20Exx, 05Bxx, 05Cxx, 16Kxx, 17Axx © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
In 1955, Chevalley [67] published constructions of simple groups of Lie type from Lie algebras. At that t
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