Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday

422 Pages·2013·2.507 MB·English

by  Alan Huckleberry, Ivan Penkov, Gregg Zuckerman (eds.)

Progress in Mathematics
306
Alan Huckleberry
Ivan Penkov
Gregg Zuckerman
Editors
Lie Groups:
Structure,
Actions, and
Representations
In Honor of Joseph A. Wolf on the
Occasion of his 75th Birthday

Progress in Mathematics
Volume306
SeriesEditors
HymanBass
JosephOesterle´
YuriTschinkel
AlanWeinstein
Alan Huckleberry (cid:129) Ivan Penkov
Gregg Zuckerman
Editors
Lie Groups: Structure,
Actions, and Representations
In Honor of Joseph A. Wolf on the Occasion
of his 75th Birthday
Editors
AlanHuckleberry IvanPenkov
FacultyofMathematics SchoolofScienceandEngineering
RuhrUniversita¨tBochum JacobsUniversity
Bochum,Germany Bremen,Germany
SchoolofScienceandEngineering
JacobsUniversity
Bremen,Germany
GreggZuckerman
DepartmentofMathematics
YaleUniversity
NewHaven,CT,USA
ISBN978-1-4614-7192-9 ISBN978-1-4614-7193-6(eBook)
DOI10.1007/978-1-4614-7193-6
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013941881
Mathematics Subject Classification (2010): 53C15, 53B15, 31B05, 32L25, 44A15, 22E46, 32M10,
32M05, 46E22, 32S55, 43A85, 21EXX, 14LXX, 16RXX, 16WXX, 22E65, 22E45, 32A25, 22E30,
58B99,58J20,58J40,20F50,19A31,57R67,32N10,20G05,13A50,43A32,43A90
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JosephA.Wolf,Oberwolfach,1984

Preface
This volume is dedicated to Joseph A. Wolf on the occasion of his 75th birthday.
ParticipantsattheconferenceinBochuminWolf’shonor,whichtookplaceinearly
January 2012, had the chance to express their respect and their thanks for Joe’s
fundamentalcontributionsto mathematicsand to wish him continuedgoodhealth
andsuccessforthecomingyears.We,theeditorsofthisvolume,wouldliketotake
thisopportunitytoputthesewishesinwriting.
Almost60ofJoe’s75yearshavebeendevotedtomathematics.Attheageof15,
hewasgrantedaFordFoundationscholarshiptobeginhisundergraduatestudiesat
theUniversityofChicago.Atfirsthisparentswereratherskepticalaboutthisidea,
butAdrianAlbert,whohadbeenafriendofJoe’sfatherintheirundergraduatedays,
calmedtheirworries.Joestartedoutinabroadliberalartsprogrambutstimulatedby
lecturesfromLang,Kaplansky,Spanier,andChern,andwiththesupportofAdrian
Albert in the background, he soon gravitated to a concentration in mathematics.
Early on Joe became particularly interested in Riemannian geometry.As a result,
with the support of an NSF Graduate Fellowship, he stayed on in Chicago to do
hisgraduateworkwithChern.CoursesfromHelgason,MacLane,Palais,Sternberg,
Stone, and Weil, in additionto those mentionedabove,broadenedhis foundation.
WhenitbecameclearthathewoulddirecthisresearchtowardRiemanniangeometry
and homogeneous spaces, he helped organize a seminar on Cartan’s work on
symmetric spaces, the members of which included Chern, Helgason, Palais, and
Sternberg.
Atthattime,thelate1950s,thespiritofthetheoryoffinitegroupswasinvading
Chicago.Forexample,JohnThompsonwasone ofJoe’s officemates. Maybethis
contributed to Joe’s optimism to suggest to Chern to consider the Clifford–Klein
sphericalspace form problem as a thesis project. Chern found a way to smoothly
indicatethatJoedidn’tyetknowenoughaboutfinitegroups.SoJoeenteredthearea
ina morerealisticway byextendingtheresultsofVincentforspherestocompact
homogeneous spaces G=K where rk.G/ D rk.K/ C 1 and G satisfies a certain
cohomologicalcondition.Later,inhisbookSpacesofConstantCurvature,nowin
its 6th edition, Joe gave the classification of complete Riemannian manifolds of
constantpositivecurvature.
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