Harmonic Analysis on Reductive Groups
A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It
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Series Editors
J. Oesterle A. Weinstein
Harmonie Analysis on Reduetive Groups
r.Bowaoin Co{[ege 1989
William Barker Pau! Sally Editors
Springer Science+Business Medi~ LLC
William H. Barker Department of Mathematies Bowdoin College Brunswiek, ME 04011
Paul J. Sal1y, Jr. Department of Mathematies University of Chieago Chieago, IL 60637
Library of Congress Cataloging-in-Publieation Data Harmonie analysis on reduetive groups: proceedings of the Bowdoin eonferenee 1989, Bowdoin College, 1989 / William Barker, Pau1 Sally, editors. p. em. -- (Progress in mathematies : vol. 101) Includes bibliographieal referenees. ISBN 978-1-4612-6768-3 ISBN 978-1-4612-0455-8 (eBook) DOI 10.1007/978-1-4612-0455-8 1. P-adie groups--Congresses. 2. Representations of groups- Congresses. 3. Harmonie analysis--Congresses. I. Barker, 11. Sal1y, Paul. III. Series. William, 1946QA 171.H32 1991 91-33801 512'.74--de20 CIP Printed on acid-free paper © Springer Science+Business Media New York 1991 Originally published by Birkhäuser Boston in 1991 Softcover reprint ofthe hardcover 1st edition 1991 Copyright is not claimed for works ofU.S. Government employees. All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission ofthe copyright owner.
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ISBN 978-1-4612-6768-3 Typeset in AMS-TE X. 987 6 5 4 3 2 1
CONTENTS
Lifting of Characters Jeffrey Adams
1
Handling the Inverse Spherical Fourier Transform Jean-Philippe Anker . . . . . . . . . .
51
Some Problems in Local Harmonic Analysis James Arthur . . . . . . . . . . . . . . . . . . . . . . . . . 57 Asymptotic Expansions on Symmetric Spaces Erik van den Ban and Henrik Schlichtkrull . . . . . . . . . . . . . 79 The Admissible Dual of GLN via Restriction to Compact Open Subgroups Colin J. Bushnell and Philip C. Kutzko
. . . . . . . . . 89
Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-Adic Group Laurent Clozel .
101
Constructing the Supercuspidal Representations of GLN(F ), F p-Adic Lawrence Corwin . . . . . . . . . . . .
123
A Remark on the Dunkl Differential Difference Operators Gerrit J. Heckman .
181
Invariant Differential Operators and Weyl Group Invariants Sigurdur Helgason . . . . . . . . . . . . . . . . .
193
The Schwartz Space of a Semisimple Lie Group Rebecca A. Herb .
201
Intertwining Functors and Irreducibility of Standard Harish-Chandra Sheaves Dragan MiIi~i(; . . . .
209
vi
Contents
Fundamental G-Strata Lawrence Morris. . .
22
