Lie Groups

Table of Contents

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   Book Overview
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   Chapter 1 Haar Measure
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   Chapter 2 Schur Orthogonality
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   Chapter 3 Compact Operators
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   Chapter 4 The Peter–Weyl Theorem
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   Chapter 5 Lie Subgroups of $$\mathrm{GL}(n, \mathbb{C})$$
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   Chapter 6 Vector Fields
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   Chapter 7 Left-Invariant Vector Fields
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   Chapter 8 The Exponential Map
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    Chapter 9 Tensors and Universal Properties
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    Chapter 10 The Universal Enveloping Algebra
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    Chapter 11 Extension of Scalars
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    Chapter 12 Representations of $$\mathfrak{s}\mathfrak{l}(2, \mathbb{C})$$
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    Chapter 13 The Universal Cover
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    Chapter 14 The Local Frobenius Theorem
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    Chapter 15 Tori
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    Chapter 16 Geodesics and Maximal Tori
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    Chapter 17 The Weyl Integration Formula
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    Chapter 18 The Root System
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    Chapter 19 Examples of Root Systems
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    Chapter 20 Abstract Weyl Groups
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    Chapter 21 Highest Weight Vectors
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    Chapter 22 The Weyl Character Formula
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    Chapter 23 The Fundamental Group
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    Chapter 24 Complexification
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    Chapter 25 Coxeter Groups
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    Chapter 26 The Borel Subgroup
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    Chapter 27 The Bruhat Decomposition
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    Chapter 28 Symmetric Spaces
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    Chapter 29 Relative Root Systems
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    Chapter 30 Embeddings of Lie Groups
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    Chapter 31 Spin
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    Chapter 32 Mackey Theory
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    Chapter 33 Characters of $$\mathrm{GL}(n, \mathbb{C})$$
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    Chapter 34 Duality Between S k and $$\mathrm{GL}(n, \mathbb{C})$$
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    Chapter 35 The Jacobi–Trudi Identity
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    Chapter 36 Schur Polynomials and $$\mathrm{GL}(n, \mathbb{C})$$
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    Chapter 37 Schur Polynomials and S k
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    Chapter 38 The Cauchy Identity
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    Chapter 39 Random Matrix Theory
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    Chapter 40 Symmetric Group Branching Rules and Tableaux
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    Chapter 41 Unitary Branching Rules and Tableaux
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    Chapter 42 Minors of Toeplitz Matrices
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    Chapter 43 The Involution Model for S k
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    Chapter 44 Some Symmetric Algebras
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    Chapter 45 Gelfand Pairs
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    Chapter 46 Hecke Algebras
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    Chapter 47 The Philosophy of Cusp Forms
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    Chapter 48 Cohomology of Grassmannians