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Progress in Mathematics 312 Monica Nevins Peter E. Trapa Editors Representations of Reductive Groups In Honor of the 60th Birthday of David A. Vogan, Jr. ProgressinMathematics Volume312 SeriesEditors HymanBass Jiang-HuaLu JosephOesterle´ YuriTschinkel Moreinformationaboutthisseriesathttp://www.springer.com/series/4848 Monica Nevins Peter E. Trapa (cid:2) Editors Representations of Reductive Groups In Honor of the 60th Birthday of David A. Vogan, Jr. Editors MonicaNevins PeterE.Trapa DepartmentofMathematicsandStatistics DepartmentofMathematics UniversityofOttawa UniversityofUtah Ottawa,ON,Canada SaltLakeCity,UT,USA ISSN0743-1643 ISSN2296-505X (electronic) ProgressinMathematics ISBN978-3-319-23442-7 ISBN978-3-319-23443-4 (eBook) DOI10.1007/978-3-319-23443-4 LibraryofCongressControlNumber:2015955838 Mathematics Subject Classification (2000): 11E72, 11F72, 14F05, 14F10, 14L24, 14M15, 14N15, 16RXX,16S30,20B35,20C08,20C20,20F55,20G05,20G07,20G20,20G99,22D10,22E25,22E30, 22E45,22E46,22E47,22E50,32C38,53C35,55N33,58A14 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia(www. springer.com) ToDavidVogan,withadmiration Contents Preface............................................................ ix TheMathematicalWorkofDavidA.Vogan,Jr.::::::::::::::::::::::: 1 WilliamM.McGovernandPeterE.Trapa Onexoticandperverse-coherentsheaves :::::::::::::::::::::::::::: 11 PramodN.Achar Parametersfortwistedrepresentations :::::::::::::::::::::::::::::: 51 JeffreyAdamsandDavidA.Vogan,Jr. LadderrepresentationsofGL.n;Q /:::::::::::::::::::::::::::::::: 117 p DanBarbaschandDanCiubotaru ArithmeticinvarianttheoryII:Pureinnerformsandobstructions totheexistenceoforbits::::::::::::::::::::::::::::::::::::::::::: 139 ManjulBhargava,BenedictH.Gross,andXiaohengWang HeckealgebraswithunequalparametersandVogan’sleftcell invariants::::::::::::::::::::::::::::::::::::::::::::::::::::::: 173 Ce´dricBonnafe´ andMeinolfGeck ThesmoothlociofspiralSchubertvarietiesoftypeAz ::::::::::::::::: 189 2 WilliamGrahamandWenjingLi Centersandcocentersof0-Heckealgebras::::::::::::::::::::::::::: 227 XuhuaHe Diraccohomology,ellipticrepresentationsandendoscopy :::::::::::::: 241 Jing-SongHuang Aprogramforbranchingproblemsintherepresentationtheoryofreal reductivegroups ::::::::::::::::::::::::::::::::::::::::::::::::: 277 ToshiyukiKobayashi vii viii Contents Equationsforafiltrationofsheetsandthevarietyofsingularelements ofacomplexsemisimpleLiealgebra :::::::::::::::::::::::::::::::: 323 BertramKostant Onconjugacyclassesinareductivegroup ::::::::::::::::::::::::::: 333 GeorgeLusztig HeckealgebrasandinvolutionsinCoxetergroups::::::::::::::::::::: 365 GeorgeLusztigandDavidA.Vogan,Jr. Comparingandcharacterizingsomeconstructionsofcanonicalbases fromCoxetersystems::::::::::::::::::::::::::::::::::::::::::::: 399 EricMarberg UppersemicontinuityofKLVpolynomials forcertainblocksofHarish-Chandramodules:::::::::::::::::::::::: 437 WilliamM.McGovern Hodgetheoryandunitaryrepresentations ::::::::::::::::::::::::::: 443 WilfriedSchmidandKariVilonen OnellipticfactorsinrealendoscopictransferI ::::::::::::::::::::::: 455 DianaShelstad OntheGelfand–Kirillovdimensionofadiscreteseriesrepresentation:::: 505 NolanR.Wallach AreduciblecharacteristicvarietyintypeA :::::::::::::::::::::::::: 517 GeordieWilliamson Preface ThisvolumeisanoutgrowthoftheconferenceRepresentationsofReductiveGroups: A conference dedicated to David Vogan on his 60th birthday, which took place at MITfromMay19–23,2014.Thiscelebratoryconferenceshowcaseddevelopments intherepresentationtheoryofreductiveLiegroupsandalgebraicgroupsoverfinite and local fields, as well as connections of this theory with other subjects, such as number theory, automorphic forms, algebraic geometry and combinatorics. It was anoccasiontomarkthe60thbirthdayofDavidVogan,whohasinspiredandshaped thedevelopmentofthisfieldforalmost40years.Alistofconferencespeakersap- pearsonpagexiii. David Vogan has proven himself a leader in the field in many ways. The most evidentofthesearehisvastandinfluentialmathematicalcontributions,anoverview of which appears in the chapter The Mathematical Work of David A. Vogan, Jr. in thisvolume.Also,ofsignificantimportancetosomany—andtouspersonally— has been David’s mentorship, insight and guidance. We include a subset of those whohavebenefittedfromworkingcloselywithDavid—namely,hisPhDstudents to date, as well as some of his mathematical descendants who were able to attend theconference—onpagesxvitoxviii. AMSCentennialFellow(1977),PlenaryLectureroftheInternationalCongress of Mathematicians (1986), Herman Weyl Lecturer (IAS, 1986), Member of the American Academy of Arts and Sciences (1996), Robert E. Collins Distinguished Scholar,MIT,(2007–2012),winneroftheLeviL.ConantPrize(2011)forhispaper “ThecharactertableofE ”,MemberoftheNationalAcademyofScience(2013), 8 andcurrentNorbertWeinerChairatMIT(2014–2019),DavidVoganhasbeenoften beendistinguishedbyhispeersandbythemathematicalcommunity.Significantly, he has also given back through substantial work in academic service, including as Head of the MIT Department of Mathematics (1999–2004) and President of the AmericanMathematicalSociety(2013–2015). Thisvolumerepresentsasteptowardsexpressingourthanks. ix

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