Lie Groups
Springer-Verlag New York Inc.
978-1-4419-1937-3 (ISBN)
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* Preface * Part I: Compact Groups: Haar Measure * Schur Orthogonality * Compact Operators * The Peter-Weyl Theorem * Part II: Lie Group Fundamentals: Lie Subgroups of GL(n, C) * Vector Fields * Left Invariant Vector Fields * The Exponential Map * Tensors and Universal Properties * The Universal Enveloping Algebra * Extension of Scalars * Representations of sl(2, C) * The Universal Cover * The Local Frobenius Theorem * Tori * Geodesics and Maximal Tori * Topological proof of Cartan's Theorem * The Weyl Integration Formula * The Root System * Examples of Root Systems * Abstract Weyl Groups * The Fundamental Group * Semisimple Compact Groups * Highest Weight Vectors * The Weyl Character Formula * Spin * Complexification * Coxeter Groups * The Iwasawa Decomposition * The Bruhat Decomposition * Symmetric Spaces * Relative Root Systems.* Embeddings of Lie Groups * Part III: Frobenius-Schur Duality: Mackey Theory * Characters of GL(n, C) * Duality between Sk and GL(n, C) * The Jacobi-Trudi Identity * Schur Polynomials and GL(n, C) * Schur Polynomials and Sk * Random Matrix Theory * Minors of Toeplitz Matrices * Branching Formulae and Tableaux * The Cauchy Identity * Unitary branching rules * The Involution Model for Sk * Some Symmetric Algebras * Gelfand Pairs * Hecke Algebras * Cohomology of Grassmannians * References
| Reihe/Serie | Graduate Texts in Mathematics ; 225 |
|---|---|
| Zusatzinfo | 32 black & white illustrations, 1 black & white tables |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 651 g |
| Einbandart | Paperback |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-4419-1937-6 / 1441919376 |
| ISBN-13 | 978-1-4419-1937-3 / 9781441919373 |
| Zustand | Neuware |
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