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

545 Pages·2016·5.795 MB·English

by  Monica Nevins, Peter E. Trapa

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
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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