Editorial Board
James E. Humphreys
Lance Small
2000 Mathematics Subject Classification. Primary 17B37.
ABSTRACT. This book is an introduction to the theory of quantum groups. Its main objects are
the quantized enveloping algebras introduced independently by Drinfeld and Jimbo. We study
their finite dimensional representations, their centers, and their bases. In particular, we look at
the crystal (or canonical) bases discovered independently by Lusztig and Kashiwara.
We first look at the quantum analogue of the Lie algebra SI2, and then at the quantum analogue
of arbitrary finite dimensional complex Lie algebras. The book is directed to anyone who wants to
learn the subject and has been introduced to the theory of finite dimensional complex Lie algebras.
Library of Congress Cataloging-in-Publication Data
Jantzen, Jens Carsten.
Lectures on quantum groups / Jens Carsten Jantzen.
p. cm. (Graduate studies in mathematics, ISSN 1065-7339; v. 6)
Includes bibliographical references and index.
ISBN 0-8218-0478-2 (alk. paper)
1. Quantum groups. 2. Mathematical physics. I. Title. II. Series.
QC20.7.G70J36 1995 95-25393
512'.55—ic20 CIP
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in teaching or research. Permission is granted to quote brief passages from this publication in
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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-permissionQams.org.
© 1996 by the American Mathematical Society. All rights reserved.
Reprinted by the American Mathematical Society, 1997, 2009.
Printed in the United States of America.
The American Mathematical Society retains all rights
except those granted to the United States Government.
@ 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 http://www.ams.org/
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