Representation Theory: Fourth International Conference on Representation Theory July 16-20, 2007, Lhasa, China

314 Pages·2009·2.183 MB·English

by  Zongzhu Lin, Jianpan Wang (ed.)

C
ONTEMPORARY
M
ATHEMATICS
478
Representation Theory
Fourth International Conference
on Representation Theory
July 16 –20, 2007
Lhasa, China
Zongzhu Lin
Jianpan Wang
Editors
American Mathematical Society
This page intentionally left blank
C
ONTEMPORARY
M
ATHEMATICS
478
Representation Theory

Fourth International Conference
on Representation Theory
July 16–20, 2007
Lhasa, China
Zongzhu Lin
Jianpan Wang
Editors
American Mathematical Society
Providence, Rhode Island
Editorial Board
Dennis DeTurck, managing editor
George Andrews Abel Klein Martin J. Strauss
2000 Mathematics Subject Classification. Primary16Gxx, 17Bxx, 20Cxx, 20Gxx;
Secondary 17B10, 17B20, 17B37, 17B45, 17B56,20G05, 20G10, 20G42,20C05, 20C08,
20C30.
Library of Congress Cataloging-in-Publication Data
Representationtheory/ZongzhuLin,JianpanWang,editors.
p.cm. —(Contemporarymathematics;v.478)
Includesbibliographicalreferences.
ISBN978-0-8218-4555-4(alk.paper)
1. Representations of algebras—Congresses. 2. Representations of groups—Congresses.
I.Lin,Zongzhu. II.Wang,Jianpan,1949– III.Title.
QA150.R46 2008
515(cid:1).7223—dc22 2008034291
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Contents
Preface vii
List of Talks ix
List of Participants xiii
Sum formulas and Ext-groups
Henning Haahr Andersen 1
Schur-Weyl duality in positive characteristic
Stephen Doty 15
The centers of Iwahori-Hecke algebras are filtered
Andrew Francis and Weiqiang Wang 29
On Kostant’s theorem for Lie algebra cohomology
University of Georgia VIGRE Algebra Group 39
G-stable pieces and partial flag varieties
Xuhua He 61
Steinbergrepresentations andduality propertiesofarithmeticgroups, mapping
class groups, and outer automorphism groups of free groups
Lizhen Ji 71
Characters of simplylaced nonconnected groups versus characters of
nonsimplylaced connected groups
Shrawan Kumar, George Lusztig, and Dipendra Prasad 99
Classification of finite-dimensional basic Hopf algebras according to their
representation type
Gongxiang Liu 103
Twelve bridges from a reductive group to its Langlands dual
G. Lusztig 125
Some new highest weight categories
Brian J. Parshall and Leonard L. Scott 145
Classification of quasi-trigonometric solutions of the classical Yang–Baxter
equation
Iulia Pop and Alexander Stolin 155
The relevance and the ubiquity of Pru¨fer modules
Claus Michael Ringel 163
v
vi CONTENTS
Quivers and the euclidean group
Alistair Savage 177
eu -Lie admissible algebras and Steinberg unitary Lie algebras
2
Shikui Shang and Yun Gao 189
Lusztig’s conjecture for finite classical groups with even characteristic
Toshiaki Shoji 207
A survey on quasifinite representations of Weyl type Lie algebras
Yucai Su 237
Maximal and primitive elements in baby Verma modules for type B
2
Nanhua Xi 257
Irreducible representations of the special algebras in prime characteristic
Yu-feng Yao and Bin Shu 273
Preface
ThefourthInternational Conference on RepresentationTheory(ICRT-
IV) was held in Lhasa, China, during July 16–20, 2007. The first three conferences
wereheldinShanghai(1998),Kunming(2001),andChengdu(2004). Themaingoal
of the ICRT is to bring together representation theorists of various subjects such
as algebraic groups, quantum groups, finite groups, Lie algebras, vertex operator
algebras, Hecke algebras and complex reflection groups, quivers, finite dimensional
algebras, Hall algebras, and other related topics. The representation theory has
evolved to connect many different fields of mathematics and the ICRT intends to
communicate the common ideas and approaches to common questions. During
the five day programs, participants have endured both mathematical and physical
challenges. There was also a two day sub-conference on Mathematical History
which covered many interesting historical topics such as early mathematics text
books in Tibet and the first Chinese national who ever obtained formal Ph.D. in
mathematics.
This volume containseighteenpapersthatmore orless reflectthetopicsof the
conference. Allpaperswerecarefullyrefereed. Severalrefereesreadseveralversions
of the manuscripts and made critical comments to ensure the high quality of the
papers. The editors want to express their sincere appreciation to all referees for
their anonymous contribution. Due to page limitation, the editors regret that not
all submitted papers are included and thank all authors for their contribution to
this proceedings.
It was a challenge from many respects to bring the conference to this ”high
level”. The conference would not be possible without many people’s hardwork.
JianpanWangandHebingRuihadtraveledtoLhasaseveraltimestoarrangehotel
andlecturefacilities. Bothof themhave beenworkingformore thanayearraising
fund for the conference and making travel arrangements for international partic-
ipants. Many participants took trains through the newly built railroad at 5 km
altitudeand thetrainride lasts formore thantwodays. Makingsuch arrangement
wasimpossiblewithoutthehelpofmanylocalmathematiciansatvariouscities. The
mathematicians in Tibet University, Da Luosang Langjie and Yutian Fei, provided
invaluablehelpmakinglocalarrangementincludingthepost-conferencetours. The
volunteer staff member, Xin Wang (a graduate student at University of Virginia),
provided an impeccable professional-type services during conference.
The financial support from the following organizations, projects, and individu-
als are greatly appreciated:
— Tianyuan Mathematical Fund, National Natural Science Foundation of
China
— “985” fund, East China Normal University
vii
viii PREFACE
— “111 Project”, Department of Mathematics, East China Normal Univer-
sity
— ChangjiangScholarsandInnovativeResearchTeam,DepartmentofMath-
ematics, East China Normal University
— JunHu,“NewCenturyExcellentTalentsinUniversity”,BeijingInstitute
of Technology
— Fang Li, “New Century Excellent Talents in University”, Zhejiang Uni-
versity
— Hebing Rui, “New Century Excellent Talents in University”, East China
Normal University
— Yucai Su, “One-Hundred Talent Program”, University of Science and
Technology of China
— Jianpan Wang, Fund of Science and Technology Commission of Shanghai
Municipality, No. 06JC 14024
— Jianpan Wang, fund of National Natural Science Foundation of China,
No. 10631010
The ICRT-IV was co-hosted by East China Normal University and the Tibet
University at Lhasa. The organizing committee consists of Jianpan Wang (Chair,
East China Normal University), Da Luosang Langjie (Co-chair, Tibet University
at Lhasa), Bangming Deng (Beijing Normal University), Yutian Fei (Tibet Uni-
versity), Jun Hu (Beijing Institute of Technology), Ruyun Ma (Northwest Normal
University), Liangang Peng (Sichuan University), Hebing Rui (East China Normal
University).
The program committee consists of Jianpan Wang (Chair, East China Nor-
mal University), Jiping Zhang (Co-chair, Peking University), Chongying Dong
(UC Santa Cruz), Jie Du (University of New South Wales), Zongzhu Lin (Kansas
State University), Yucai Su (The University of Science and Technology of Chi-
nese), Weiqiang Wang (University of Virginia), Nanhua Xi (Academy Sinica), Jie
Xiao (Tsinghua University).
Lastbutnotleast,theeditorswanttothankChristineM.Thivierge,Associate
Editor for Proceedings at American Mathematical Society who worked so closely
and patiently with the editors to ensure the timely publication of this proceedings.
Zongzhu Lin
Jianpan Wang
June 2008