紧李群的表示（影印版）

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作　者：	Theodor Brocker,Tammo tom Dieck
出版社：	北京世图
丛编项：	Graduate Texts in Mathematics
标　签：	群与组合编码

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ISBN：	9787506201278	出版时间：	2004-06-01	包装：	胶版纸
开本：	24开	页数：	313	字数：

内容简介

　　This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras， though mentioned occasionally， are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago.本书为英文版。

作者简介

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图书目录

CHAPTERI
LieGroupsandLieAlgebras
1.TheConceptofaLieGroupandtheClassicalExamples
2.Left-InvariantVectorFieldsandOne-ParameterGroups
3.TheExponentialMap
4.HomogeneousSpacesandQuotientGroups
5.InvariantIntegration
6.CliffordAlgebrasandSpinorGroups
CHAPTERII
ElementaryRepresentationTheory
1.Representations
2.SemisimpleModules
3.LinearAlgebraandRepresentations
4.CharactersandOrthogonalityRelations
5.RepresentationsofSU(2),SO(3),U(2),andO(3).
6.RealandQuaternionicRepresentations
7.TheCharacterRingandtheRepresentationRing
8.RepresentationsofAbelianGroups
9.RepresentationsofLieAlgebras
10.TheLieAlgebrasl(2,C)
CHAPTERIII
RepresentativeFunctions
1.AlgebrasofRepresentativeFunctions
2.SomeAnalysisonCompactGroups
3.TheTheoremofPeterandWeyl
4.ApplicationsoftheTheoremofPeterandWeyl
5.GeneralizationsoftheTheoremofPeterandWeyl
6.InducedRepresentations
7.Tannaka-KreinDuality
8.TheComplexificationofCompactLieGroups
CHAPTERIV
TheMaximalTorusofaCompactLieGroup
1.MaximalTori
2.ConsequencesoftheConjugationTheorem
3.TheMaximalToriandWeylGroupsoftheClassicalGroups
4.CartanSubgroupsofNonconnectedCompactGroups
CHAPTERV
RootSystems
1.TheAdjointRepresentationandGroupsofRank1
2.RootsandWeylChambers
3.RootSystems
4.BasesandWeylChambers
5.DynkinDiagrams
6.TheRootsoftheClassicalGroups
7.TheFundamentalGroup,theCenterandtheStiefetDiagram
8.TheStructureoftheCompactGroups
CHAPTERVI
IrreducibleCharactersandWeights
1.TheWeylCharacterFormula
2.TheDominantWeightandtheStructureoftheRepresentationRing
3.TheMultiplicitiesoftheWeightsofanIrreducibleRepresentation
4.RepresentationsofRealorQuaternionicType
5.RepresentationsoftheClassicalGroups
6.RepresentationsoftheSpinorGroups
7.RepresentationsoftheOrthogonalGroups
Bibliography
SymbolIndex
SubjectIndex