Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honor of Roger E Howe (Lecture Notes Series, Institute for Mathematical Sciences National University of Singapore)

446 Pages·2008·2.446 MB·English

by  Jian-Shu Li (editor), Eng-Chye Tan (editor), Chen-Bo Zhu (editor), Nolan R Wallach (editor)

HARMONIC ANALYSIS,
GROUP REPRESENTATIONS, AUTOMORPHIC FORMS
AND INVARIANT THEORY
In Honor of Roger E. Howe
LECTURE NOTES SERIES
Institute for Mathematical Sciences, National University of Singapore
Series Editors: Louis H. Y. Chen and Ka Hin Leung
Institute for Mathematical Sciences
National University of Singapore
ISSN: 1793-0758
Published
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edited by Harald Niederreiter
Vol. 2 Representations of Real and p-Adic Groups
edited by Eng-Chye Tan & Chen-Bo Zhu
Vol. 3 Selected Topics in Post-Genome Knowledge Discovery
edited by Limsoon Wong & Louxin Zhang
Vol. 4 An Introduction to Stein’s Method
edited by A. D. Barbour & Louis H. Y. Chen
Vol. 5 Stein's Method and Applications
edited by A. D. Barbour & Louis H. Y. Chen
Vol. 6 Computational Methods in Large Scale Simulation
edited by K.-Y. Lam & H.-P. Lee
Vol. 7 Markov Chain Monte Carlo: Innovations and Applications
edited by W. S. Kendall, F. Liang & J.-S. Wang
Vol. 8 Transition and Turbulence Control
edited by Mohamed Gad-el-Hak & Her Mann Tsai
Vol. 9 Dynamics in Models of Coarsening, Coagulation, Condensation
and Quantization
edited by Weizhu Bao & Jian-Guo Liu
Vol. 10 Gabor and Wavelet Frames
edited by Say Song Goh, Amos Ron & Zuowei Shen
Vol. 11 Mathematics and Computation in Imaging Science and
Information Processing
edited by Say Song Goh, Amos Ron & Zuowei Shen
Vol. 12 Harmonic Analysis, Group Representations, Automorphic Forms
and Invariant Theory — In Honor of Roger E. Howe
edited by Jian-Shu Li, Eng-Chye Tan, Nolan Wallach & Chen-Bo Zhu
LaiFun - Harmonic Analysis.pmd 2 10/1/2007, 2:14 PM
Lecture Notes Series, Institute for Mathematical Sciences, Vol.
12
National University of Singapore
HARMONIC ANALYSIS,
GROUP REPRESENTATIONS, AUTOMORPHIC FORMS
AND INVARIANT THEORY
In Honor of Roger E. Howe
Editors
Jian-Shu Li
Hong Kong University of Science & Technology, Hong Kong
Eng-Chye Tan
National University of Singapore, Singapore
Nolan Wallach
University of California, San Diego, USA
Chen-Bo Zhu
National University of Singapore, Singapore
World Scientific
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Lecture Notes Series, Institute for Mathematical Sciences,
National University of Singapore — Vol. 12
HARMONIC ANALYSIS, GROUP REPRESENTATIONS, AUTOMORPHIC
FORMS AND INVARIANT THEORY
In Honor of Roger E. Howe
Copyright © 2007 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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For photocopying of material in this volume, please pay a copying fee through the Copyright
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ISBN-13 978-981-277-078-3
ISBN-10 981-277-078-X
Printed in Singapore.
LaiFun - Harmonic Analysis.pmd 1 10/1/2007, 2:14 PM
CONTENTS
Foreword vii
Preface ix
The Theta Correspondence over R
Je(cid:11)rey Adams 1
The Heisenberg Group, SL(3;R), and Rigidity
Andreas C(cid:20)ap, Michael G. Cowling, Filippo De Mari,
Michael Eastwood and Rupert McCallum 41
Pfa(cid:14)ans and Strategies for Integer Choice Games
Ron Evans and Nolan Wallach 53
When is an L-Function Non-Vanishing in Part of the
Critical Strip?
Stephen Gelbart 73
CohomologicalAutomorphic Forms on Unitary Groups, II:
Period Relations and Values of L-Functions
Michael Harris 89
The Inversion Formula and Holomorphic Extension of the
Minimal Representation of the Conformal Group
Toshiyuki Kobayashi and Gen Mano 151
Classi(cid:12)cation des S(cid:19)eries Discr(cid:18)etes pour Certains Groupes
Classiques p-Adiques
Colette M(cid:27)glin 209
Some Algebras of Essentially Compact Distributions of a
Reductive p-Adic Group
Allen Moy and Marko Tadi(cid:19)c 247
v
vi Contents
Annihilators of Generalized Verma Modules of the Scalar Type
for Classical Lie Algebras
Toshio Oshima 277
Branching to a Maximal Compact Subgroup
David A. Vogan, Jr. 321
Small Semisimple Subalgebras of Semisimple Lie Algebras
Jeb F. Willenbring and Gregg J. Zuckerman 403
FOREWORD
The Institute for Mathematical Sciences at the National University of
Singaporewasestablishedon1July2000. Itsmissionistofostermathemat-
icalresearch,particularlymultidisciplinaryresearchthatlinksmathematics
tootherdisciplines,tonurturethegrowthofmathematicalexpertiseamong
researchscientists,totraintalentforresearchinthemathematicalsciences,
and to provide a platform for interaction and collaboration between local
and foreign mathematical scientists, in support of national development.
TheInstituteorganizesthematicprogramswhichlastfromonemonthto
sixmonths. Thethemeorthemesofaprogramwillgenerallybeofamulti-
disciplinarynature,chosenfromareasattheforefrontofcurrentresearchin
the mathematical sciences and their applications, and in accordance with
the scienti(cid:12)c interests and technological needs in Singapore.
Generally,foreachprogramtherewillbetutoriallecturesonbackground
material followed by workshops at the research level. Notes on these lec-
tures are usually made available to the participants for their immediate
bene(cid:12)t during the program. The main objective of the Institutes Lecture
Notes Series is to bring these lectures to a wider audience. Occasionally,
the Series may also include the proceedings of workshops and expository
lectures organized by the Institute.
The World Scienti(cid:12)c Publishing Company has kindly agreed to pub-
lish the Lecture Notes Series. This Volume, \Harmonic Analysis, Group
Representations, Automorphic Forms and Invariant Theory: In Honor of
Roger E. Howe", is the twelfth of this Series. We hope that through the
regularpublicationoftheselecturenotesthe Institutewillachieve,inpart,
its objective of promoting research in the mathematical sciences and their
applications.
May 2007 Louis H. Y. Chen
Ka Hin Leung
Series Editors
vii
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
PREFACE
Roger E. Howe, member of the National Academy of Sciences, USA and
fellow of the American Academy of Arts and Sciences, and Professor of
Mathematics at Yale University, is a scholar of distinction.
Howe’s major research interest is in applications of symmetry, parti-
cularly harmonic analysis, group representations, automorphic forms and
invariant theory. To honor Howe’s exceptional achievements both as a
scholar and a teacher, an International Conference on Harmonic Analysis,
GroupRepresentations,AutomorphicFormsandInvariantTheorywasheld
at the National University of Singapore (NUS) from January 9 - 11, 2006,
on the occasion of his 60th birthday.
ThefactthattheconferencewasheldinSingaporeandhadmanyatten-
dees from the Asia-Paci(cid:12)c region is clearly (cid:12)tting due to Howe’s extensive
contact with and signi(cid:12)cant in(cid:13)uence within the region. He has on many
occasions visited universities in Australia, Israel, Japan, Singapore, Hong
KongandChina. Inparticular,hewasafellowoftheInstituteforAdvanced
Studies at Hebrew University in Jerusalem in 1988, a fellow of the Japan
SocietyfortheAdvancementofSciencein1993andiscurrentlychairofthe
Scienti(cid:12)cAdvisoryBoardofthe Institute forMathematicalSciences(IMS)
in NUS.
Thespeakersof the conferenceareMichaelCowling(Universityof New
South Wales, Australia), Stephen Gelbart (Weizmann Institute, Israel),
Michael Harris (Universit(cid:19)e Paris VII, France), Masaki Kashiwara and
Toshiyuki Kobayashi(both of RIMS, Kyoto University, Japan), Hanspeter
Kraft (Universita(cid:127)t Basel, Switzerland), Colette Moeglin (Universit(cid:19)e Paris
VII,France),AllenMoy(HongKongUniversityofScienceandTechnology,
HongKong),ToshioOshima(UniversityofTokyo,Japan),WilfriedSchmid
(Harvard University, USA), David Vogan (MIT, USA), Gregg Zuckerman
(Yale University, USA).
The eleven articles of this volume are for the most part expanded from
theinvitedlecturesoftheConferenceandareallreviewed. Inthefollowing,
ix