导语

  

内容提要

  

    本书是一部很受欢迎的教材，初版于1991年，至今已被Springer出版社重印5次。全书分为四部分，26章，书中主要论述李群、李代数和经典群的有限维表示， 可作为大学高年级学生, 研究生及教师的教学用书。
    （一）有限群：有限群表示；特征；实例；Ed表示；Ud 、GL2和 Fq表示；外尔结构。（二）李群和李代数：李群；李代数和李群；李代数的初始分类；一维、二维和三维中的李代数；sl2 C表示；sl3 C表示。（三）经典李代数及其示；任意半单李代数的结构与表示； Sl4 C和sln C；辛李代数；Sp6C和sp2n C；正交李代数；So6 C、 So7 C和som C；so m C自旋表示。（四）李理论：复单李群的分类；G2和其它例外李代数；复李群；外尔特征公式；实李代数和李群。
    读者对象：数学及物理学专业的高年级本科生、研究生和教师。

Preface
Using This Book
Part Ⅰ: Finite Groups
1. Representations of Finite Groups
  1.1: Definitions
  1.2: Complete Reducibility; Schur's Lemma
  1.3: Examples: Abelian Groups; □3
2. Characters
  2.1: Characters
  2.2: The First Projection Formula and Its Consequences
  2.3: Examples: □4 and 9.□4
  2.4: More Projection Formulas; More Consequences
3. Examples; Induced Representations; Group Algebras; Real Representations
  3.1: Examples: □5 and □4
  3.2: Exterior Powers of the Standard Representation of □d
  3.3: Induced Representations
  3.4: The Group Algebra
  3.5: Real Representations and Representations over Subfields of C
4. Representations of □4： Young Diagrams and Frobenius's Character Formula
  4.1: Statements of the Results
  4.2: Irreducible Representations of □4
  4.3: Proof of Frobenius's Formula
5. Representations of □d and GL2(Fq)
  5.1: Representations of □4
  5.2: Representations of GL2(Fq) and SL2(Fq)
6. Weyl's Construction
  6.1: Schur Functors and Their Characters
  6.2: The Proofs
Part Ⅱ: Lie Groups and Lie Algebras
7. Lie Groups
  7.1: Lie Groups: Definitions
  7.2: Examples of Lie Groups
  7.3: Two Constructions
8. Lie Algebras and Lie Groups
  8.1: Lie Algebras: Motivation and Definition
  8.2: Examples of Lie Algebras
  8.3: The Exponential Map
9. Initial Classification of Lie Algebras
  9.1: Rough Classification of Lie Algebras
  9.2: Engel's Theorem and Lie's Theorem
  9.3: Semisimple Lie Algebras
  9.4: Simple Lie Algebras
10. Lie Algebras in Dimensions One, Two, and Three
  10.1: Dimensions One and Two
  10.2: Dimension Three, Rank 1
  10.3: Dimension Three, Rank 2
  10.4: Dimension Three, Rank 3
11. Representations of sl2C
  11.1: The Irreducible Representations
  11.2: A Little Plethysm
  11.3: A Little Geometric Plethysm
……
Part Ⅲ: The Classical Lie Algebras and Their Representations
Appendices