The Genesis of the Langlands Program PDF
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LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorEndreSu¨li,MathematicalInstitute,UniversityofOxford,WoodstockRoad, OxfordOX26GG,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat www.cambridge.org/mathematics 358 Geometricandcohomologicalmethodsingrouptheory,M.R.BRIDSON,P.H.KROPHOLLER& I.J.LEARY(eds) 359 Modulispacesandvectorbundles,L.BRAMBILA-PAZ,S.B.BRADLOW,O.GARC´IA-PRADA&S. RAMANAN(eds) 360 Zariskigeometries,B.ZILBER 361 Words:Notesonverbalwidthingroups,D.SEGAL 362 Differentialtensoralgebrasandtheirmodulecategories,R.BAUTISTA,L.SALMERO´N&R.ZUAZUA 363 Foundationsofcomputationalmathematics,HongKong2008,F.CUCKER,A.PINKUS&M.J.TODD (eds) 364 Partialdifferentialequationsandfluidmechanics,J.C.ROBINSON&J.L.RODRIGO(eds) 365 Surveysincombinatorics2009,S.HUCZYNSKA,J.D.MITCHELL&C.M.RONEY-DOUGAL(eds) 366 Highlyoscillatoryproblems,B.ENGQUIST,A.FOKAS,E.HAIRER&A.ISERLES(eds) 367 Randommatrices:Highdimensionalphenomena,G.BLOWER 368 GeometryofRiemannsurfaces,F.P.GARDINER,G.GONZA´LEZ-DIEZ&C.KOUROUNIOTIS(eds) 369 Epidemicsandrumoursincomplexnetworks,M.DRAIEF&L.MASSOULIE´ 370 Theoryofp-adicdistributions,S.ALBEVERIO,A.YU.KHRENNIKOV&V.M.SHELKOVICH 371 Conformalfractals,F.PRZYTYCKI&M.URBAN´SKI 372 Moonshine:Thefirstquartercenturyandbeyond,J.LEPOWSKY,J.MCKAY&M.P.TUITE(eds) 373 Smoothness,regularityandcompleteintersection,J.MAJADAS&A.G.RODICIO 374 Geometricanalysisofhyperbolicdifferentialequations:Anintroduction,S.ALINHAC 375 Triangulatedcategories,T.HOLM,P.JØRGENSEN&R.ROUQUIER(eds) 376 Permutationpatterns,S.LINTON,N.RUSˇKUC&V.VATTER(eds) 377 AnintroductiontoGaloiscohomologyanditsapplications,G.BERHUY 378 Probabilityandmathematicalgenetics,N.H.BINGHAM&C.M.GOLDIE(eds) 379 Finiteandalgorithmicmodeltheory,J.ESPARZA,C.MICHAUX&C.STEINHORN(eds) 380 Realandcomplexsingularities,M.MANOEL,M.C.ROMEROFUSTER&C.T.CWALL(eds) 381 Symmetriesandintegrabilityofdifferenceequations,D.LEVI,P.OLVER,Z.THOMOVA& P.WINTERNITZ(eds) 382 Forcingwithrandomvariablesandproofcomplexity,J.KRAJ´IEK 383 Motivicintegrationanditsinteractionswithmodeltheoryandnon-Archimedeangeometry I,R.CLUCKERS,J.NICAISE&J.SEBAG(eds) 384 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryII, R.CLUCKERS,J.NICAISE&J.SEBAG(eds) 385 EntropyofhiddenMarkovprocessesandconnectionstodynamicalsystems,B.MARCUS, K.PETERSEN&T.WEISSMAN(eds) 386 Independence-friendlylogic,A.L.MANN,G.SANDU&M.SEVENSTER 387 GroupsStAndrews2009inBathI,C.M.CAMPBELLetal(eds) 388 GroupsStAndrews2009inBathII,C.M.CAMPBELLetal(eds) 389 Randomfieldsonthesphere,D.MARINUCCI&G.PECCATI 390 Localizationinperiodicpotentials,D.E.PELINOVSKY 391 Fusionsystemsinalgebraandtopology,M.ASCHBACHER,R.KESSAR&B.OLIVER 392 Surveysincombinatorics2011,R.CHAPMAN(ed) 393 Non-abelianfundamentalgroupsandIwasawatheory,J.COATESetal(eds) 394 Variationalproblemsindifferentialgeometry,R.BIELAWSKI,K.HOUSTON&M.SPEIGHT(eds) 395 Howgroupsgrow,A.MANN 396 Arithmeticdifferentialoperatorsoverthep-adicintegers,C.C.RALPH&S.R.SIMANCA 397 Hyperbolicgeometryandapplicationsinquantumchaosandcosmology,J.BOLTE&F.STEINER(eds) 398 Mathematicalmodelsincontactmechanics,M.SOFONEA&A.MATEI 399 Circuitdoublecoverofgraphs,C.-Q.ZHANG 400 Densespherepackings:ablueprintforformalproofs,T.HALES 401 AdoubleHallalgebraapproachtoaffinequantumSchur–Weyltheory,B.DENG,J.DU&Q.FU 402 Mathematicalaspectsoffluidmechanics,J.C.ROBINSON,J.L.RODRIGO&W.SADOWSKI(eds) 403 Foundationsofcomputationalmathematics,Budapest2011,F.CUCKER,T.KRICK,A.PINKUS& A.SZANTO(eds) 404 Operatormethodsforboundaryvalueproblems,S.HASSI,H.S.V.DESNOO&F.H.SZAFRANIEC (eds) 405 Torsors,e´talehomotopyandapplicationstorationalpoints,A.N.SKOROBOGATOV(ed) 406 Appalachiansettheory,J.CUMMINGS&E.SCHIMMERLING(eds) 407 Themaximalsubgroupsofthelow-dimensionalfiniteclassicalgroups,J.N.BRAY,D.F.HOLT&C.M. RONEY-DOUGAL 408 Complexityscience:theWarwickmaster’scourse,R.BALL,V.KOLOKOLTSOV&R.S.MACKAY (eds) 409 Surveysincombinatorics2013,S.R.BLACKBURN,S.GERKE&M.WILDON(eds) 410 Representationtheoryandharmonicanalysisofwreathproductsoffinitegroups, T.CECCHERINI-SILBERSTEIN,F.SCARABOTTI&F.TOLLI 411 Modulispaces,L.BRAMBILA-PAZ,O.GARC´IA-PRADA,P.NEWSTEAD&R.P.THOMAS(eds) 412 Automorphismsandequivalencerelationsintopologicaldynamics,D.B.ELLIS&R.ELLIS 413 Optimaltransportation,Y.OLLIVIER,H.PAJOT&C.VILLANI(eds) 414 AutomorphicformsandGaloisrepresentationsI,F.DIAMOND,P.L.KASSAEI&M.KIM(eds) 415 AutomorphicformsandGaloisrepresentationsII,F.DIAMOND,P.L.KASSAEI&M.KIM(eds) 416 Reversibilityindynamicsandgrouptheory,A.G.O’FARRELL&I.SHORT 417 Recentadvancesinalgebraicgeometry,C.D.HACON,M.MUSTAT¸A˘ &M.POPA(eds) 418 TheBloch–KatoconjecturefortheRiemannzetafunction,J.COATES,A.RAGHURAM,A.SAIKIA& R.SUJATHA(eds) 419 TheCauchyproblemfornon-Lipschitzsemi-linearparabolicpartialdifferentialequations,J.C.MEYER &D.J.NEEDHAM 420 Arithmeticandgeometry,L.DIEULEFAITetal(eds) 421 O-minimalityandDiophantinegeometry,G.O.JONES&A.J.WILKIE(eds) 422 GroupsStAndrews2013,C.M.CAMPBELLetal(eds) 423 Inequalitiesforgrapheigenvalues,Z.STANIC´ 424 Surveysincombinatorics2015,A.CZUMAJetal(eds) 425 Geometry,topologyanddynamicsinnegativecurvature,C.S.ARAVINDA,F.T.FARRELL& J.-F.LAFONT(eds) 426 Lecturesonthetheoryofwaterwaves,T.BRIDGES,M.GROVES&D.NICHOLLS(eds) 427 RecentadvancesinHodgetheory,M.KERR&G.PEARLSTEIN(eds) 428 GeometryinaFre´chetcontext,C.T.J.DODSON,G.GALANIS&E.VASSILIOU 429 Sheavesandfunctionsmodulop,L.TAELMAN 430 RecentprogressinthetheoryoftheEulerandNavier-Stokesequations,J.C.ROBINSON, J.L.RODRIGO,W.SADOWSKI&A.VIDAL-LO´PEZ(eds) 431 Harmonicandsubharmonicfunctiontheoryontherealhyperbolicball,M.STOLL 432 Topicsingraphautomorphismsandreconstruction(2ndEdition),J.LAURI&R.SCAPELLATO 433 RegularandirregularholonomicD-modules,M.KASHIWARA&P.SCHAPIRA 434 Analyticsemigroupsandsemilinearinitialboundaryvalueproblems(2ndEdition),K.TAIRA 435 GradedringsandgradedGrothendieckgroups,R.HAZRAT 436 Groups,graphsandrandomwalks,T.CECCHERINI-SILBERSTEIN,M.SALVATORI& E.SAVA-HUSS(eds) 437 Dynamicsandanalyticnumbertheory,D.BADZIAHIN,A.GORODNIK&N.PEYERIMHOFF(eds) 438 Randomwalksandheatkernelsongraphs,M.T.BARLOW 439 Evolutionequations,K.AMMARI&S.GERBI(eds) 440 Surveysincombinatorics2017,A.CLAESSONetal(eds) 441 Polynomialsandthemod2SteenrodalgebraI,G.WALKER&R.M.W.WOOD 442 Polynomialsandthemod2SteenrodalgebraII,G.WALKER&R.M.W.WOOD 443 Asymptoticanalysisingeneralrelativity,T.DAUDE´,D.HA¨FNER&J.-P.NICOLAS(eds) 444 Geometricandcohomologicalgrouptheory,P.H.KROPHOLLER,I.J.LEARY,C.MART´INEZ-PE´REZ &B.E.A.NUCINKIS(eds) 445 Introductiontohiddensemi-Markovmodels,J.VANDERHOEK&R.J.ELLIOTT 446 Advancesintwo-dimensionalhomotopyandcombinatorialgrouptheory,W.METZLER& S.ROSEBROCK(eds) 447 Newdirectionsinlocallycompactgroups,P.-E.CAPRACE&N.MONOD(eds) 448 Syntheticdifferentialtopology,M.C.BUNGE,F.GAGO&A.M.SANLUIS 449 Permutationgroupsandcartesiandecompositions,C.E.PRAEGER&C.SCHNEIDER 450 Partialdifferentialequationsarisingfromphysicsandgeometry,M.BENAYEDetal(eds) 451 Topologicalmethodsingrouptheory,N.BROADDUS,M.DAVIS,J.-F.LAFONT&I.ORTIZ(eds) 452 Partialdifferentialequationsinfluidmechanics,C.L.FEFFERMAN,J.C.ROBINSON&J.L.RODRIGO (eds) 453 Stochasticstabilityofdifferentialequationsinabstractspaces,K.LIU 454 Beyondhyperbolicity,M.HAGEN,R.WEBB&H.WILTON(eds) 455 GroupsStAndrews2017inBirmingham,C.M.CAMPBELLetal(eds) 456 Surveysincombinatorics2019,A.LO,R.MYCROFT,G.PERARNAU&A.TREGLOWN(eds) 457 Shimuravarieties,T.HAINES&M.HARRIS(eds) 458 IntegrablesystemsandalgebraicgeometryI,R.DONAGI&T.SHASKA(eds) 459 IntegrablesystemsandalgebraicgeometryII,R.DONAGI&T.SHASKA(eds) 460 Wigner-typetheoremsforHilbertGrassmannians,M.PANKOV 461 Analysisandgeometryongraphsandmanifolds,M.KELLER,D.LENZ&R.K.WOJCIECHOWSKI 462 ZetaandL-functionsofvarietiesandmotives,B.KAHN 463 Differentialgeometryinthelarge,O.DEARRICOTTetal(eds) 464 Lecturesonorthogonalpolynomialsandspecialfunctions,H.S.COHL&M.E.H.ISMAIL(eds) 465 ConstrainedWillmoresurfaces,A´.C.QUINTINO 466 Invarianceofmodulesunderautomorphismsoftheirenvelopesandcovers,A.K.SRIVASTAVA, A. TUGANBAEV&P.A.G.ASENSIO 467 ThegenesisoftheLanglandsprogram,J.MUELLER&F.SHAHIDI “It is exciting to read this important book. It is a marvelous panorama of the life, work, and inspiration of Robert Langlands, as he discovered and developedhisgrandideas,andasheguidedhisstudents.Theseideasnowlargely shape the broad architecture of representation theory and automorphic forms, creatingagrandbridgebetweenanalysisandarithmetic–withconnectionsto mathematicalphysics.Thecontributorstothisvolumeofferus–andwillsurely offerfuturehistoriansofourmathematicalage–asplendidintroductionto,and overviewof,theearlydaysofLanglands’program.” –BarryMazur,HarvardUniversity Robert Langlands was born in 1936, in New Westminster, British Columbia. Hereceivedhisbachelor’sandmaster’sdegreesinmathematicsattheUniver- sityofBritishColumbiain1958,andhisPh.D.fromYaleUniversityin1960. HenotonlypassedhisoralexaminationbutalsosubmittedhisPh.D.thesisat theendofhisfirstyearatYale. TheinceptionoftheLanglandsProgramcanbedatedto1967.In1972,he wasappointedprofessorattheInstituteforAdvancedStudyinPrinceton,New Jersey,USA,wherehehasbeenaProfessorEmeritus. ProfessorLanglandshasreceivednumerousprestigiousawards,suchasthe 1996WolfPrize(withAndrewWiles)andthe2007ShawPrize(withRichard Taylor).Heisalsotherecipientofthe2018AbelPrize,whichhasoftenbeen regardedastheequivalentofthe“NobelPrize”inmathematics. RobertLanglandsandhiswife,Charlotte,havebeenlivinginCanadasince March2020. The Genesis of the Langlands Program Editedby JULIA MUELLER FordhamUniversity,NewYork FREYDOON SHAHIDI PurdueUniversity,Indiana UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre, NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108710947 DOI:10.1017/9781108591218 ©CambridgeUniversityPress2021 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2021 PrintedintheUnitedKingdombyTJBooksLimited,PadstowCornwall AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. ISBN978-1-108-71094-7Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Contents ListofContributors pageix Preface xi Introduction xii PARTI REMEMBRANCEOFTHINGSPAST 1 1 AGlimpseattheGenesisoftheLanglandsProgram 3 JuliaMueller 2 TheEarlyLanglandsProgram–PersonalReflections 43 SteveGelbart PARTII LANGLANDSASMENTOR 57 3 LanglandsandTurkey 59 CihanSac¸liog˘lu 4 ReminiscencesbyaStudentofLanglands 65 ThomasHales 5 GraduateSchoolwithLanglands 70 S.AliAltug˘ 6 MyUnforgettableEarlyYearsattheInstitute:Enstitu¨de UnutulmazErkenYıllarım 74 DinakarRamakrishnan PARTIII LANGLANDSASFRIEND 83 7 MyReminiscencesofBobLanglandsattheUniversity ofBritishColumbia 85 AlanGoodacre 8 RobertP.Langlands:l’hommederrie`relemathe´maticien 88 ClaudeLevesque vii viii Contents 9 Unhommedecultureetdenature 100 ClaudePichet PARTIV SURVEYSOFTHELANGLANDSPROGRAM– EARLYYEARS 107 10 AnIntroductiontoLanglandsFunctoriality 109 JamesArthur 11 IntheBeginning:Langlands’DoctoralThesis 130 DerekW.Robinson 12 TheLanglandsSpectralDecomposition 176 Jean-PierreLabesse 13 AutomorphicRepresentationsandL-FunctionsforGL(n) 215 DorianGoldfeldandHerve´ Jacquet 14 AutomorphicL-Functions 275 FreydoonShahidi 15 LanglandsReciprocity:L-Functions,AutomorphicForms, andDiophantineEquations 301 MatthewEmerton 16 OnSomeEarlySourcesfortheNotionofTransferin LanglandsFunctoriality:PartIAnOverviewwithExamples 387 DianaShelstad PARTV LANGLANDS’CONTRIBUTIONSTO MATHEMATICALPHYSICS 401 17 RobertLanglands’WorkinMathematicalPhysics 403 ThomasSpencer 18 L’invarianceconformeetl’universalite´ aupointcritiquedes mode`lesbidimensionnels 414 YvanSaint-Aubin Contributors S.AliAltug˘ BostonUniversity JamesArthur UniversityofToronto MatthewEmerton UniversityofChicago SteveGelbart WeizmannInstituteofScience DorianGoldfeld ColumbiaUniversity AlanGoodacre DominionObservatory,Ottawa(retired) ThomasHales UniversityofPittsburgh Herve´ Jacquet ColumbiaUniversity Jean-PierreLabesse MarseilleInstituteofMathematics ix
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