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Vladimir Dobrev
Editor
Lie Theory and Its
Applications in Physics
IX International Workshop
123
Editor
VladimirDobrev
InstituteforNuclearResearch
andNuclearEnergy
BulgarianAcademyofSciences
72TsarigradskoChaussee
Sofia,Bulgaria
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-4-431-54269-8 ISBN978-4-431-54270-4(eBook)
DOI10.1007/978-4-431-54270-4
SpringerTokyoHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013934220
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Preface
The workshop series “Lie Theory and Its Applications in Physics” is designed
to serve the community of theoretical physicists, mathematical physicists, and
mathematicians working on mathematical models for physical systems based on
geometricalmethodsandinthefieldofLietheory.
The series reflects the trend towards a geometrization of the mathematical
description of physical systems and objects. A geometric approach to a system
yieldsingeneralsomenotionofsymmetrywhichisveryhelpfulinunderstanding
its structure. Geometrizationand symmetriesare meantin their widest sense, i.e.,
classical geometry, differential geometry, groups and quantum groups, infinite-
dimensional (super-)algebras, and their representations. Furthermore, we include
the necessary tools from functional analysis and number theory. This is a big
interdisciplinaryandinterrelatedfield.
The first three workshopswere organizedin Clausthal (1995, 1997, 1999),the
4thwaspartofthe2ndSymposium“QuantumTheoryandSymmetries”inCracow
(2001),the 5th,7th, and8th were organizedin Varna(2003,2007,2009),andthe
6th was part of the 4th Symposium “Quantum Theory and Symmetries” in Varna
(2005)buthasitsownvolumeofproceedings.
The9thworkshopoftheseries(LT-9)wasorganizedbytheInstituteofNuclear
ResearchandNuclearEnergyoftheBulgarianAcademyofSciences(BAS)inJune
2011 (20–26), at the guest house of BAS near Varna on the Bulgarian Black Sea
Coast.
Theoverallnumberofparticipantswas76andtheycamefrom21countries.
The scientific level was very high as can be judged by the speakers. The
plenaryspeakerswereAntonAlekseev(Geneva),LorianoBonora(Trieste),Branko
Dragovich (Belgrade), Anthony Joseph (Rehovot), Toshiyuki Kobayashi (Tokyo),
Jean-Louis Loday (Strasbourg), Ivan Penkov (Bremen), Karl-Henning Rehren
(Gttingen),andIvanTodorov(Sofia).Aspecialplenarysession, withthe speakers
Joris Van der Jeugt (Ghent), Ronald King (Southampton), and David Finkelstein
(Atlanta), was devoted to the 75th-year Jubilee of Tchavdar Palev, Professor
EmeritusatourInstitute.
v
vi Preface
The topics covered the most modern trends in the field of the workshop:
representationtheory,quantumfield theory,string theory,(super-)gravitytheories,
conformal field theory, supersymmetry, quantum groups, vertex algebras, and
integrability.
The members of the International Organizing Committee were V.K. Dobrev
(Sofia)andH.-D.Doebner(Clausthal),incollaborationwithG.Rudolph(Leipzig).
ThemembersoftheLocalOrganizingCommitteewereV.K.Dobrev(Chairman),
V.I. Doseva, A. Ganchev, S.G. Mihov, D. Nedanovski, T.V. Popov, T. Stefanova,
M.N.Stoilov,andS.T.Stoimenov.
Acknowledgments
We expressourgratitudeto the Institute of NuclearResearch andNuclearEnergy
and to the Abdus Salam InternationalCentre for Theoretical Physics for financial
help. We thank the BulgarianAcademyof Sciencesfor providingits guesthouse,
whichcontributedverymuchtothestimulatingandpleasantatmosphereduringthe
workshop.Wethankthepublisher,SpringerJapan,representedbyMs.ChinoHasebe
(Executive Editor in Mathematics, Statistics, Business, Economics, Computer
Science) and Mr. Masayuki Nakamura (Editorial Department), for assistance in
thispublication.Lastbutnotleast,wethankthemembersoftheLocalOrganizing
Committee, who, through their efforts, made the workshop run smoothly and
efficiently.
SofiaandGeneva VladimirDobrev
Contents
PartI PlenaryTalks
ALumpSolutioninSFT ........................................................ 3
LorianoBonora
Towardsp-AdicMatterintheUniverse ....................................... 13
BrankoDragovich
PalevStatisticsandtheChronon............................................... 25
DavidRitzFinkelstein
SomeRemarksonWeierstrassSections,AdaptedPairs
andPolynomiality................................................................ 39
AnthonyJoseph
FromPalev’sStudy ofWigner QuantumSystemstoNew
ResultsonSumsofSchurFunctions........................................... 61
RonaldC.King
VarnaLectureonL2-AnalysisofMinimalRepresentations................. 77
ToshiyukiKobayashi
ExponentialSeriesWithoutDenominators ................................... 95
Jean-LouisLoday
NewMethodsinConformalPartialWaveAnalysis.......................... 109
ChristophNeumann,Karl-HenningRehren,andLenaWallenhorst
EuclideanConfigurationSpaceRenormalization,Residues
andDilationAnomaly ........................................................... 127
NikolayM.Nikolov,RaymondStora,andIvanTodorov
WignerQuantizationandLieSuperalgebraRepresentations .............. 149
JorisVanderJeugt
vii
viii Contents
PartII QuantumFieldTheory
Spontaneous Breaking of Supersymmetry, Localization
andNicolaiMappinginMatrixModels ....................................... 169
FumihikoSugino
MirrorMapasGeneratingFunctionofIntersectionNumbers............. 181
MasaoJinzenji
OperadicConstructionoftheRenormalizationGroup...................... 191
Jean-LouisLodayandNikolayM.Nikolov
PartIII StringandGravityTheories
LightlikeBraneworldsinAnti-deSitterBulkSpace-Times................. 215
EduardoGuendelman,AlexanderKaganovich,EmilNissimov,
andSvetlanaPacheva
GeneralizedBernoulliPolynomialsandtheCasimir Effect
intheEinsteinUniverse ......................................................... 231
PatrickMoylan
FromSingularitiestoAlgebrastoPureYang–MillswithMatter........... 239
TamarFriedmann
OnModifiedGravity............................................................. 251
IvanDimitrijevic,BrankoDragovich,JelenaGrujic,andZoranRakic
PartIV QuantumGroupsandRelatedObjects
Theq-WakimotoRealizationoftheSuperalgebrasU (s(cid:2)l(N|1))
q
andU (s(cid:2)l(N|1)) ................................................................. 263
q,p
TakeoKojima
QuantumPhasesinNoncommutativeSpace.................................. 277
O¨.F.DayiandB.Yapıs¸kan
OnQuantumWZNW MonodromyMatrix:Factorization,
Diagonalization,andDeterminant ............................................. 287
LudmilHadjiivanovandPaoloFurlan
PartV RepresentationTheory
SomePropertiesofPlanarGalileanConformalAlgebras................... 301
NaruhikoAizawa
InvariantDifferentialOperatorsforNon-compactLieGroups:
TheSp(n,IR)Case................................................................ 311
V.K.Dobrev
Contents ix
GeneralizationoftheGell–MannDecontractionFormula
forsl(n,R)andItsApplicationsinAffineGravity ........................... 337
IgorSalomandDjordjeSˇijacˇki
W-AlgebrasExtendingg(cid:2)l(1|1).................................................. 349
ThomasCreutzigandDavidRidout
Non-LocalSpace-TimeTransformationsGenerated
fromtheAgeingAlgebra........................................................ 369
StoimenStoimenovandMalteHenkel
ConstructionoftheNoncommutativeRankIBergmanDomain........... 381
ZhituoWang
PartVI VertexAlgebras
SingularVectorsandZhu’sPoissonAlgebraofParafermion
VertexOperatorAlgebras....................................................... 391
TomoyukiArakawa,ChingHungLam,andHiromichiYamada
Boson-FermionCorrespondenceofTypeBandTwistedVertex
Algebras........................................................................... 399
IanaI.Anguelova
On Twisted Modules for N=2 Supersymmetric Vertex
OperatorSuperalgebras......................................................... 411
KatrinaBarron
PartVII IntegrabilityandOtherApplications
The Ruijsenaars Self-Duality Map as a Mapping Class
Symplectomorphism............................................................. 423
L.Fehe´randC.Klimcˇ´ık
Hilbert Space Decomposition for Coulomb Blockade
inFabry–Pe´rotInterferometers................................................ 439
LachezarS.Georgiev
GroupClassificationofVariableCoefficientKdV-likeEquations.......... 451
OlenaVaneeva
ANewDiffeomorphismSymmetryGroupofMagnetohydrodynamics.... 461
AsherYahalom
InvariancePropertiesoftheExceptionalQuantumMechanics
(F )andItsGeneralizationtoComplexJordanAlgebras(E ) ............. 469
4 6
SultanCatto,YoonS.Choun,andLeventKurt
MatrixSuperpotentials.......................................................... 477
YuriKaradzhov
