Elements of the Theory of Representations
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the orig
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Editors
S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf S. Mac Lane W. Magnus M.M. Postnikov F. K. Schmidt W. Schmidt D. S. Scott K. Stein J. Tits B. L. van der Waerden Managing Editors B. Eckmann
J.K. Moser
A. A. Kirillov
Elements of the Theory of Representations
Translated from the Russian by Edwin Hewitt
Springer-Verlag Berlin Heidelberg New York 1976
Aleksandr A. Kirillov Moscow State University Edwin Hewitt University of Washington
Title of the Russian Original Edition: Elementy Teorii Predstavlenil Publisher: Nauka, Moscow, 1972
AMS Subject Classifications (1970): Primary43-xx Secondary 20Cxx, 22A25, 22Dxx, 22Exx, 81A17, 81A78
ISBN-13: 978-3-642-66245-4 DOl: 10.1 007/978-3-642-66243-0
e-ISBN-13: 978-3-642-66243-0
Library of Congress Cataloging in Publication Data. Kirillov, Aleksandr Aleksandrovich, 1936-. Elements of the theory of representations (Grundlehren der mathematischen Wissenscharten; 220). Translation of Elementy teorii predstavlenii. Bibliography: p. Includes index. 1. Representations of groups. I. Title. II. Series: Die Grundlehren der mathematischen Wissenscharten in Einzeldarstellung; 220. QA171. K5213. 512'.22. 75-31705 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under ยง 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. C by Springer-Verlag Berlin Heidelberg 1976 Softcover reprint of the hardcover I st edition 1976 Typesetting and printing: Zechnersche Buchdruckerei. Speyer
Bookbinding: Konrad Trillsch, Wiirzburg
Translator's Preface
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The transl
