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 ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.birkhauser-science.com) 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. ix