Lie Group Representations I Proceedings of the Special Year held at

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Lie Group Representations I Proceedings of the Special Year held at the University of Maryland, College Park, 1982-1983

Edited by R. Herb, R. Lipsman and J. Rosenberg



Spri nger-Verlag Berlin I-Ieidelberg New York Tokyo 1983

Editors Rebecca Herb Ronald Lipsman Jonathan Rosenberg Department of Mathematics, University of Maryland College Park, MD 20742, USA

AMS Subject Classifications (1980): 22E47, 22E40, 17B35 ISBN 3-540-12725-9 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-12725-9 Springer-Verlag New York Heidelberg Berlin Tokyo Library of Congress Cataloging in Publication Data Main entry under title: Lie group representations. (Lecture notes in mathematics; 1024) Sponsored by the Dept. of Mathematics, University of Maryland, College Park. 1. Lie groups-Congresses. 2. Representations of groups-Congresses. I. Herb, R. (Rebecca), 1948-. II. Lipsman, Ronald L. III. Rosenberg, J. (Jonathan), 1951-. IV. University of Maryland, College Park. Dept. of Mathematics. V. Series: Lecture notes in mathematics (Springer-Verlag); 1024. OA3.L28 no. 1024 510s [512'.55] 83-16871 [OA387] ISBN 0-387-12725-9 (U.S. : v. 1) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1983 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210

PREFACE The Department of Hathematics of the University of

con-

ducted a Special Year in Lie Group Representations during the academic year 1982­1983.

This

containing articles

submitted by the main speakers during the Special Year.

110st of the

invited speakers submitted articles, and virtually all of those appearing here deal with the subject matter on which the authors lectured during their visits to !1aryland. The Special Year program at Haryland represents a thriving departmental tradition­­this being the fourteenth consecutive year in which such an event has taken place.

usual, the subject matter vras chosen

on the basis of active current research and the interests of departmental members. ject.

The modern theory of Lie r,roup Representations is a vast sub-

In order to keep the program within bounds, the Special Year was

planned around five distinct intensive periods of activity­­each one (of three weeks duration) devoted to one of the main branches of current research in the subject.

During those periods (approximately)

distinguished researchers were invited to present lecture series on areas of current interest.

Each visitor spent 1­3 weeks in the depart-

ment and gave 2­5 lectures.

In addition, during each period approxi-

mately 8­10 other visitors received financial support in order to attend and pa