Author | Bump, Daniel. author |
---|---|
Title | Lie Groups [electronic resource] / by Daniel Bump |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-4094-3 |
Descript | XI, 454 p. 32 illus. online resource |
1 Haar Measure -- 2 Schur Orthogonality -- 3 Compact Operators -- 4 The Peter-Weyl Theorem -- 5 Lie Subgroups of GL(n, ?) -- 6 Vector Fields -- 7 Left-Invariant Vector Fields -- 8 The Exponential Map -- 9 Tensors and Universal Properties -- 10 The Universal Enveloping Algebra -- 11 Extension of Scalars -- 12 Representations of sl(2, ?) -- 13 The Universal Cover -- 14 The Local Frobenius Theorem -- 15 Tori -- 16 Geodesics and Maximal Tori -- 17 Topological Proof of Cartanโs Theorem -- 18 The Weyl Integration Formula -- 19 The Root System -- 20 Examples of Root Systems -- 21 Abstract Weyl Groups -- 22 The Fundamental Group -- 23 Semisimple Compact Groups -- 24 Highest-Weight Vectors -- 25 The Weyl Character Formula -- 26 Spin -- 27 Complexification -- 28 Coxeter Groups -- 29 The Iwasawa Decomposition -- 30 The Bruhat Decomposition -- 31 Symmetric Spaces -- 32 Relative Root Systems -- 33 Embeddings of Lie Groups -- 34 Mackey Theory -- 35 Characters of GL(n, ?) -- 36 Duality between Sk and GL(n, ?) -- 37 The Jacobi-Trudi Identity -- 38 Schur Polynomials and GL(n, ?) -- 39 Schur Polynomials and Sk -- 40 Random Matrix Theory -- 41 Minors of Toeplitz Matrices -- 42 Branching Formulae and Tableaux -- 43 The Cauchy Identity -- 44 Unitary Branching Rules -- 45 The Involution Model for Sk -- 46 Some Symmetric Algebras -- 47 Gelfand Pairs -- 48 Hecke Algebras -- 49 The Philosophy of Cusp Forms -- 50 Cohomology of Grassmannians -- References