Introduction to Complex Reflection Groups and Their Braid Groups

toComplexRe ectionGroups and Their Braid Groups 123 Michel Broue Universite Paris Diderot Paris 7 UFR de Mathematiques 175 Rue du Chevaleret 75013 Paris France broue@math. jussieu. fr ISBN: 978-3-642-11174-7 e-ISBN: 978-3-642-11175-4 DOI: 10. 1007/978-3-642-11175-4 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2009943837 Mathematics Subject Classi cation (2000): 20, 13, 16, 55 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, speci cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro lm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of aspeci c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover illustration: c Anouk Grinberg Cover design: SPi Publisher Services Printed on acid-free paper springer. com Preface Weyl groups are ?nite groups acting as re?ection groups on rational vector spaces. It iswellknownthat theserationalre?ectiongroupsappearas"ske- tons" of many important mathematical objects: algebraic groups, Hecke algebras, Artin-Tits braid groups, etc.