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[美] 克里斯 (Chiss N.) 著 / 世界图书出版公司 / 2012-01 / 平装
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表示论和复几何
《表示论和复几何》是一部经典的从集合角度讲述表示论的高等教程。从几何的角度研究表示论,真可谓“千呼万呼始出来”,尤其是自从1980年D-模型和1990年量子群的箭图,此方法显得更为迫切。表示论的发展顺应科学发展趋势,并且都成功地应用于好多领域,如量子群、仿射李群和量子场论。《表示论和复几何》的前半部分是架起李理论标准知识初学者和数学工作者所需要的广阔背景知识之间的桥梁,为后半部分的学习做好充分的准备。
refacechapter0.introductionchapter1.symplecticgeometry1.1.symplecticmanifolds1.2.poissonalgebras1.3.poissonstructuresarisingfromnoncommutativealgebras1.4.themomentmap1.5.coisotropicsubvarieties1.6.lagrangianfamilieschapter2.mosaic2.1.hilbert'snullste!lensatz2.2.atonealgebraicvarieties2.3.thedeformationconstruction2.4.c*-actionsonaprojectivevariety2.5.fixedpointreduction2.6.borel-moorehomology2.7.convolutioninborel-moorehomologychapter3.complexsemisimplegroups3.1.semisimpleliealgebrasandflagvarieties3.2.nilpotentcone3.3.thesteinbergvariety3.4.lagrangianconstructionoftheweylgroup3.5.geometricanalysisofh(z)-action3.6.irreduciblerepresentationsofwe1groups3.7.applicationsofthejacobson-morozovtheoremchapter4.springertheoryforu(sln)4.1.geometricconstructionoftheenvelopingalgebrau(sin(c))4.2.finite-dimensionalsimplesln(c)-modules4.3.proofofthemaintheorem4.4.stabilizationchapter5.equivariantk-theory5.1.equivariantresolutions5.2.basick-theoreticconstructions5.3.specializationinequivariantk-theory5.4.thekoszulcomplexandthethomisomorphism5.5.cellularfibrationlemma5.6.thek/innethformula5.7.projectivebundletheoremandbeilinsonresolution5.8.thecherncharacter5.9.thedimensionfiltrationand"devissage"5.10.thelocalizationtheorem5.11.functorialitychapter6.flagvarieties,k-theory,andharmonicpolynomials6.1.equivariantk-theoryoftheflagvariety6.2.equivariantk-theoryofthesteinbergvariety6.3.harmonicpolynomials6.4.w-harmonicpolynomialsandflagvarieties6.5.orbitalvarieties6.6.theequivarianthilbertpolynomial6.7.kostant'stheoremonpolynomialringschapter7.heckealgebrasandk-theory7.1.affineweylgroupsandheckealgebras7.2.maintheorems7.3.caseq=hdeformationargument7.4.hilbertpolynomialsandorbitalvarieties7.5.theheckealgebraforsl27.6.pwofofthemaintheoremchapter8.representationsofconvolutionalgebras8.1.standardmodules8.2.characterformulaforstandardmodules8.3.constructiblecomplexes8.4.perversesheavesandtheclassificationtheorem8.5.thecontravariantform8.6.shed-theoreticanalysisoftheconvolutionalgebra8.7.projectivemodulesoverconvolutionalgebra8.8.anon-vanishingresult8.9.semi-smallmapsbibliography
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开播时间:09月02日 10:30