Rolf Berndt Representations of Linear Groups Rolf Berndt Representations of Linear Groups An Introduction Based on Examples from Physics and Number Theory Bibliografische information published by Die Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutschen Nationalbibliografie; detailed bibliographic data is available in the Internet at . Prof. Dr. Rolf Berndt Department of Mathematics University of Hamburg Bundesstraße 55 D-20146 Hamburg Germany
[email protected] Mathematics Subject Classification 20G05, 22E45, 20C25, 20C35, 11F70 First edition, July 2007 All rights reserved © Friedr. Vieweg & Sohn Verlag | GWV Fachverlage GmbH, Wiesbaden 2007 Editorial Office: Ulrike Schmickler-Hirzebruch | Susanne Jahnel Vieweg is a company in the specialist publishing group Springer Science+Business Media. www.vieweg.de No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder. Cover design: Ulrike Weigel, www.CorporateDesignGroup.de Printing and binding: MercedesDruck, Berlin Printed on acid-free paper Printed in Germany ISBN 978-3-8348-0319-1 Preface There are already many good books on representation theory for all kinds of groups. Two of the best (in this author’s opinion) are the one by A.W. Knapp: “Representation Theory for Semisimple Groups. An Overview based on Examples” [Kn1] and by G.W. Mackey: “Induced Representations in Physics, Probability and Number Theory” [Ma1]. The title of this text is a mixture of both these titles, and our text is meant as a very elementary introduction to these and, moreover, to