Author | Fulton, William. author |
---|---|
Title | Representation Theory [electronic resource] : A First Course / by William Fulton, Joe Harris |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0979-9 |
Descript | XV, 551 p. online resource |
I: Finite Groups -- 1. Representations of Finite Groups -- 2. Characters -- 3. Examples; Induced Representations; Group Algebras; Real Representations -- 4. Representations of: $$ {\mathfrak{S}_d}$$ Young Diagrams and Frobeniusโs Character Formula -- 5. Representations of $$ {\mathfrak{A}_d}$$ and $$ G{L_2}\left( {{\mathbb{F}_q}} \right)$$ -- 6. Weylโs 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 -- ยงA.1: Basic Symmetric Polynomials and Relations among Them -- ยงA.2: Proofs of the Determinantal Identities -- ยงA.3: Other Determinantal Identities -- B. On Multilinear Algebra -- ยงB.1: Tensor Products -- ยงB.2: Exterior and Symmetric Powers -- ยงB.3: Duals and Contractions -- C. On Semisimplicity -- ยงC.1: The Killing Form and Caftanโs Criterion -- ยงC.2: Complete Reducibility and the Jordan Decomposition -- ยงC.3: On Derivations -- D. Cartan Subalgebras -- ยงD.1: The Existence of Cartan Subalgebras -- ยงD.2: On the Structure of Semisimple Lie Algebras -- ยงD.3: The Conjugacy of Cartan Subalgebras -- ยงD.4: On the Weyl Group -- E. Adoโs and Leviโs Theorems -- ยงE.1: Leviโs Theorem -- ยงE.2: Adoโs Theorem -- F. Invariant Theory for the Classical Groups -- ยงF.1: The Polynomial Invariants -- ยงF.2: Applications to Symplectic and Orthogonal Groups -- ยงF.3: Proof of Capelliโs Identity -- Hints, Answers, and References -- Index of Symbols