Lie Groups
Springer-Verlag New York Inc.
978-0-387-21154-1 (ISBN)
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This book proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and offers a carefully chosen range of material designed to give readers the bigger picture. It explores compact Lie groups through a number of proofs and culminates in a "topics" section that takes the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as unifying them.
Haar Measure.- Schur Orthogonality.- Compact Operators.- The Peter-Weyl Theorem.- 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.- 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.
| Erscheint lt. Verlag | 9.8.2004 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; Vol.225 |
| Zusatzinfo | 32 black & white illustrations, 1 black & white tables |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 911 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-387-21154-3 / 0387211543 |
| ISBN-13 | 978-0-387-21154-1 / 9780387211541 |
| Zustand | Neuware |
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