EDITORIAL COMMITTEE Jerry L. Bona (Chair) Jean-Luc Brylinski Nigel J. Hitchin Nicolai Reshetikhin Ar−1-GATA (1) KEIRYOSHIGUN NO HYOGENRON TO KUMIAWASERON (REPRESENTATION OF QUANTUM ALGEBRAS OF TYPE A(1) r−1 AND COMBINATORICS OF YOUNG TABLEAUX) by Susumu Ariki Originally published in Japanese by Sophia University, Tokyo, 2000 Translated from the Japanese and revised by the author 2000 Mathematics Subject Classification. Primary 05E10, 17B37, 17B67, 20C08 Secondary 14M15, 16D90, 16G20, 20C33. Library of Congress Cataloging-in-Publication Data Ariki, Susumu, 1959– Representations of quantum algebras and combinatorics of Young tableaux / Susumu Ariki [translated from the Japanese and revised by the author]. p. cm. (University lecture series, ISSN 1047-3998 v. 26) Includes bibliographical references and index. ISBN 0-8218-3232-8 (acid-free paper) 1. Quantum groups. 2. Representations of groups. 3. Bases (Linear topological spaces) 4. Young tableaux. I. Title. II. University lecture series (Providence, R.I.) 26. QA176 .A7513 2002 530.14 3—dc21 2002025869 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permission@ams.org. c 2002 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02
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