Algebraic Geometry IV Linear Algebraic Groups Invariant Theory
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory ha
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Editor-in-Chief: R. V. Gamkrelidze
A. N. Parshin I.R. Shafarevich (Eds.)
Algebraic Geometry IV Linear Algebraic Groups Invariant Theory
Springer-Verlag Berlin Heidelberg GmbH
Consulting Editors of the Series: A. A. Agrachev, A. A. Gonchar, E. F. Mishchenko, N.M. Ostianu, Y.P. Sakharova, A.B. Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, VoI. 55, Aigebraicheskaya geometriya 4 Publisher VINITI, Moscow 1989
Mathematics Subject Classification (1991 ):
20Cxx,1IE57,20Gxx ISBN 978-3-642-08119-4
Library of Congress Cataloging-in-Publication Data Algebraicheskaia geometriia 4. English Algebraic geometry IV: linear algebraic groups, invariant theory / A. N. Parshin, 1. R. Shafarevich (eds.). p. cm. - (Encyclopaedia of mathematical sciences; v. 55) Includes bibliographical references and index. ISBN 978-3-642-08119-4 ISBN 978-3-662-03073-8 (eBook) DOI 10.1007/978-3-662-03073-8 1. Linear algebraic groups. 2. Invariants. 1. Parshin, A. N. Il. Shafarevich, 1. R. (lgor' Rostislavovich). 1923 III. Title. IV. Title: Algebraic geometry 4. V. Title: Algebraic geometry four. VI. Series. QA 179.A4413 1994 512'.2-dc20 93- 13928 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication ofthis publication or parts thereof is permitted only under the provisions ofthe German Copyright Law ofSeptember 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1994 Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover 1st edition 1994 Typesetting: Asco Trade Typesetting Ltd .. Hong Kong SPIN: 10013453 41/3140 - 5 432 I 0- Printed on acid-free paper
List of Editors, Authors and Translators Editor-in-Chief R. V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia
Consulting Editors A. N. Parshin, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Russia 1. R. Shafarevich, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Russia
Authors V. L. Popov, Chair of Algebra, Department of Mathematics, MIEM, Bolshoj Vuzovskij Per. 3/12,109028 Moscow, Russia T. A. Springer, Mathematisch Instituut, Rijksuniversiteit Utrecht, Postbus 80.010, 3508 T A Utrecht, The Netherlands E. B. Vinberg, Chair of Algebra, Moscow State University, 119899 Moscow, Russia
Translator of Part II G. A. Kandall, 230 Hill Street, Hamden, CT 06514-1522, USA
Contents I. Linear Algebraic Groups T. A. Springer 1 II. Invariant Theory V. L. Popov, E. B. Vinberg 123 Author Index 27
