Asymptotic Combinatorics with Applications to Mathematical Physics A
At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite
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Anatoly M. Vershik (Ed.)
Asymptotic Combinatorics with Applications to Mathematical Physics A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia July 9-20, 2001
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Editor Anatoly M. Vershik St. Petersburg Department of the Mathematical Institute Russian Academy of Sciences Fontanka 27 St. Petersburg 191011, Russia e-mail: [email protected] http://www.pdmi.ras.ru/˜vershik Technical Editor Yuri Yakubovich St. Petersburg Department of the Mathematical Institute Russian Academy of Sciences Fontanka 27 St. Petersburg 191011, Russia e-mail: [email protected]
Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 46-XX, 05-XX, 60-XX, 35-XX ISSN 0075-8434 ISBN 3-540-40312-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de c Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors SPIN: 10933565
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Preface
A European Mathematical Summer School entitled “ASYMPTOTIC COMBINATORICS WITH APPLICATIONS TO MATHEMATICAL PHYSICS” was held at St. Petersburg, Russia, 9–22 July 2001. This meeting was at the same time a NATO Advanced Studies Institute. It was cosponsored by NATO Science Committee, European Mathematical Society, and Russian Fund for Basic Research. This volume contains mathematical lectures from the school. Another part of the materials presented at the School, more related to mathematical physics, is already published1 . Information about the School, its participants, program, etc. can be found at the end of this volume. The present volume contains lecture courses, as well as several separate lectures, which have mainly mathematical rather than physical orientation. They are aimed mostl
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