Representations of Reductive Groups: In Honor of the 60th Birthday of David A. Vogan, Jr. PDF
Preview Representations of Reductive Groups: In Honor of the 60th Birthday of David A. Vogan, Jr.
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. 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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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