內容大鋼
本書是一部很受歡迎的教材，初版于1991年，至今已被Springer出版社重印5次。全書分為四部分，26章，書中主要論述李群、李代數和經典群的有限維表示， 可作為大學高年級學生, 研究生及教師的教學用書。
（一）有限群：有限群表示；特徵；實例；Ed表示；Ud 、GL2和 Fq表示；外爾結構。（二）李群和李代數：李群；李代數和李群；李代數的初始分類；一維、二維和三維中的李代數；sl2 C表示；sl3 C表示。（三）經典李代數及其示；任意半單李代數的結構與表示； Sl4 C和sln C；辛李代數；Sp6C和sp2n C；正交李代數；So6 C、 So7 C和som C；so m C自旋表示。（四）李理論：復單李群的分類；G2和其它例外李代數；復李群；外爾特徵公式；實李代數和李群。
讀者對象：數學及物理學專業的高年級本科生、研究生和教師。
目錄
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
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