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Viser: Representation Theory - A First Course
Representation Theory
A First Course
William Fulton og Joe Harris
(1991)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 3. Udgave
- Paperback: 551 sider
- Udgiver: Springer New York (Oktober 1991)
- Forfattere: William Fulton og Joe Harris
- ISBN: 9780387974958
1. Representations of Finite Groups.-
2. Characters.-
3. Examples; Induced Representations; Group Algebras; Real Representations.-
4. Representations of:$${\mathfrak{S}_d}$$Young Diagrams and Frobenius's Character Formula.-
5. Representations of$${\mathfrak{A}_d}$$and$$G{L_2}\left( {{\mathbb{F}_q}} \right)$$.-
6. Weyl's Construction.- II: Lie Groups and Lie Algebras.-
7. Lie Groups.-
8. Lie Algebras and Lie Groups.-
9. Initial Classification of Lie Algebras.-
10. Lie Algebras in Dimensions One, Two, and Three.-
11. Representations of$$\mathfrak{s}{\mathfrak{l}_2}\mathbb{C}$$.-
12. Representations of$$\mathfrak{s}{\mathfrak{l}_3}\mathbb{C},$$
Part I.-
13. Representations of$$\mathfrak{s}{\mathfrak{l}_3}\mathbb{C},$$
Part II: Mainly Lots of Examples.- III: The Classical Lie Algebras and Their Representations.-
14. The General Set-up: Analyzing the Structure and Representations of an Arbitrary Semisimple Lie Algebra.-
15.$$\mathfrak{s}{\mathfrak{l}_4}\mathbb{C}$$and$$\mathfrak{s}{\mathfrak{l}_n}\mathbb{C}$$.-
16. Symplectic Lie Algebras.-
17.$$\mathfrak{s}{\mathfrak{p}_6}\mathbb{C}$$and$$\mathfrak{s}{\mathfrak{p}_2n}\mathbb{C}$$.-
18. Orthogonal Lie Algebras.-
19.$$\mathfrak{s}{\mathfrak{o}_6}\mathbb{C},$$$$\mathfrak{s}{\mathfrak{o}_7}\mathbb{C},$$and$$\mathfrak{s}{\mathfrak{o}_m}\mathbb{C}$$.-
20. Spin Representations of$$\mathfrak{s}{\mathfrak{o}_m}\mathbb{C}$$.- IV: Lie Theory.-
21. The Classification of Complex Simple Lie Algebras.-
22. $${g_2}$$and Other Exceptional Lie Algebras.-
23. Complex Lie Groups; Characters.-
24. Weyl Character Formula.-
25. More Character Formulas.-
26. Real Lie Algebras and Lie Groups.- Appendices.- A. On Symmetric Functions.- §A.1: Basic Symmetric Polynomials and Relations among Them.- §A.2: Proofs of the Determinantal Identities.- §A.3: Other Determinantal Identities.- B. On Multilinear Algebra.- §B.1: Tensor Products.- §B.2: Exterior and Symmetric Powers.- §B.3: Duals and Contractions.- C. On Semisimplicity.- §C.1: The Killing Form and Caftan's Criterion.- §C.2: Complete Reducibility and the Jordan Decomposition.- §C.3: On Derivations.- D. Cartan Subalgebras.- §D.1: The Existence of Cartan Subalgebras.- §D.2: On the Structure of Semisimple Lie Algebras.- §D.3: The Conjugacy of Cartan Subalgebras.- §D.4: On the Weyl Group.- E. Ado's and Levi's Theorems.- §E.1: Levi's Theorem.- §E.2: Ado's Theorem.- F. Invariant Theory for the Classical Groups.- §F.1: The Polynomial Invariants.- §F.2: Applications to Symplectic and Orthogonal Groups.- §F.3: Proof of Capelli's Identity.- Hints, Answers, and References.- Index of Symbols.