Polynomial Representations of GLn
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symme
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Lecture Notes in Mathematics
J. A. Green
Polynomial Representations of GLn
830 Second Edition With an Appendix on Schensted Correspondence and Littelmann Paths By K. Erdmann, J. A. Green and M. Schocker
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
830
J.A. Green
Polynomial Representations of GLn 2nd corrected and augmented edition
with an Appendix on Schensted Correspondence and Littelmann Paths by K. Erdmann, J.A. Green and M. Schocker
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Author and co-authors for the appendix James A. Green 19 Long Close Oxford OX2 9SG United Kingdom e-mail: [email protected]
Manfred Schocker Department of Mathematics University of Wales Swansea Singleton Park, Swansea SA2 8PP United Kingdom e-mail: [email protected]
Karin Erdmann Mathematical Institute University of Oxford 24-29 St Giles Oxford OX1 3LB United Kingdom e-mail: [email protected]
Library of Congress Control Number: 2006934862 Mathematics Subject Classification (2000): Primary: 20C30, 20G05, 20G15, 16S50, 17B99, 05E10 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-46944-3 Springer Berlin Heidelberg New York ISBN-13 978-3-540-46944-5 Springer Berlin Heidelberg New York DOI 10.1007/3-540-46944-3 This work is subject to copyright. All 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 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, 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. Typesetting by the authors using a Springer LATEX package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
SPIN: 11008118
VA41/3100/SPi
543210
Preface to the second edition
This second edition of “Polynomial representations of GLn (K)” consists of two parts. The first part is a corrected version of the original text, formatted in LATEX, and retaining the original numbering of sections, equations, etc. The second is an Appendix, which is largely independent of the first part, but which leads to an algebra L(n, r), defined by P. Littelmann, which is analogous to the Schur algebra S(n, r). It is hoped that, in the future, there will be a structure theory of L(n, r) rather like that which underlies the construction of Kac-Moody Lie algebras. We use two operators which act on “words”. The fir
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