紧李群的表示
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作者(德)T.布罗克(Theodor Brocker) 著 著
出版社世界图书出版公司
ISBN9787510063855
出版时间2017-01
装帧平装
开本其他
定价55元
货号1201495920
上书时间2024-11-13
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作者简介
Theodor Brocker，Tammo tom Dieck是德国有名数学家，写有多部著作，本书是数学研究生丛书之98卷。
目录
CHAPTER Ⅰ
Lie Groups and Lie Algebras
1.The Concept of a Lie Group and the Classical Examples
2.Left—Invariant Vector Fields and One—Parameter Groups
3.The Exponential Map
4.Homogeneous Spaces and Quotient Groups
5.Invariant Integration
6.Clifford Algebras and Spinor Groups
CHAPTER Ⅱ
Elementary Representation Theory
1.Representations
2.Semisimple Modules
3.Linear Algebra and Representations
4.Characters and Ortho Sonality Relations
5.Representations of SU（2）， SO（3）， U（2）， and O（3）.
6.Real and Quaternionic Representations
7.The Character Ring and the Representation Ring
8.Representation of Abelian Groups
9.Representations of Lie Algebras
10.The Lie Algebra sl（2，C）
CHAPTER Ⅲ
Representative Functions
1.Algebras of Representative Functions
2.Some Analysis on Compact Groups
3.The Theorem of Peter and Weyl
4.Applications of the Theorem of Peter and Weyl
5.Generalizations of the Theorem of Peter and Weyl
6.Induced Representations
7.Tannaka—Krein Duality
8.The Complexification of Compact Lie Groups
CHAPTER Ⅳ
The Maximal Torus of a Compact Lie Group
1.Maximal Tori
2.Consequences of the Conjugation Theorem
3.The Maximal Tori and Weyl Groups of the Classical Groups
4.Cartan Subgroups of Nonconnected Compact Oroups
CHAPTER Ⅴ
Root Systems
1.The Adjoint Representation and Groups of Rank I
2.Roots and Weyl Chambers
3.Root Systems
4.Bases and Weyl Chambers
5.Dynkin Diagrams
6.The Roots of the Classical Groups
7.The Fundamental Group， the Center and the Stiefel Diagram
8.The Structure of the Compact C，roups
CHAPTER Ⅵ
Irreducible Characters and Weights
1.The Weyl Character Formula
2.The Dominant Weight and the Structure of the Representation Ring
3.The Multiplicities of the Weights of an Irreducible Representation
4.Representations of Real or Quatemionic Type
5.Representations of the Classical Groups
6.Representations of the Spinor Groups
7.Representations of the Orthogonal Groups
Bibliography
Symbol Index
Subject Index
内容摘要
这本书是基于作者1966年以来的讲义撰写而成，主要介绍紧李群理论。该书主要由六部分组成，每部分又有不同的章节构成，每章最后还有让读者自测的小练习。目次：李群和李代数；理论的基本表示；代表性的函数；紧李群的优选圆环体；根的形式；不可约的字符和变量；字符索引。读者对象：大学高年级本科生，低年级研究生。
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