Contents
XI
Chapter 14. Lie Groups and Their Representations 357
§14.1. Topological Groups 358
§14.2. Compact Topological Groups 363
§14.3. Lie Groups and Lie Algebras 376
§14.4. Lie Algebras 385
§14.5. Structure of Semisimple Lie Algebras 392
§14.6. Representations of sl2(C) 400
§14.7. Representations of Semisimple Lie Algebras 404
§14.8. Compact Semisimple Groups 409
Exercises 416
Chapter 15. Algebraic Groups 419
§15.1. Algebraic Groups and Their Representations 419
§15.2. Quotients and Group Actions 423
§15.3. Existence of the Quotient 427
§15.4. Jordan Decomposition 430
§15.5. Tori 433
§15.6. Solvable Algebraic Groups 437
§15.7. Semisimple Groups and Borel Subgroups 442
§15.8. Complex Semisimple Lie Groups 451
Exercises 456
Chapter 16. The Borel-Weil-Bott Theorem 459
§16.1. Vector Bundles and Induced Representations 460
§16.2. Equivariant Line Bundles on the Flag Variety 464
§16.3. The Casimir Operator 469
§16.4. The Borel-Weil Theorem 474
§16.5. The Borel-Weil-Bott Theorem 478
§16.6. Consequences for Real Semisimple Lie Groups 483
§16.7. Infinite Dimensional Representations 484
Exercises 493
Bibliography 497
Index 501
Previous Page Next Page