緊李群的表示

內(nèi)容概要

This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras, though mentioned occasionally, are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago.

書籍目錄

CHAPTER Ⅰ Lie Groups and Lie Algebras   1. The Concept of a Lie Group and the Classical Examples   2. Left-Invariant Vector Fields and One-Parameter Groups   3. The Exponential Map   4. Homogeneous Spaces and Quotient Groups   5. Invariant Integration   6. Clifford Algebras and Spinor Groups CHAPTER Ⅱ Elementary Representation Theory   1. Representations   2. Semisimple Modules   3. Linear Algebra and Representations   4. Characters and Orthogonality Relations   5. Representations of SU(2)， SO(3)， U(2)， and O(3).   6. Real and Quaternionic Representations   7. The Character Ring and the Representation Ring   8. Representations of Abelian Groups   9. Representations of Lie Algebras   10. The Lie Algebra sl(2， C) CHAPTER Ⅲ Representative Functions  1. Algebras of Representative Functions  2. Some Analysis on Compact Groups  3. The Theorem of Peter and Wey1  4. Applications of the Theorem of Peter and Wey1  5. Generalizations of the Theorem of Peter and Wey1  6. Induced Representations  7. Tannaka-Krein Duality  8. The Complexification of Compact lie CroupsCHAPTER Ⅳ The Maximal Torus of a Compact Lie Group  1. Maximal Tori  2. Consequences of the Conjugation Theorem  3. The Maximal Tori and Wey1 Groups of the Classical Groups  4. Cartan Subgroups of Nonconnected Compact GroupsCHAPTER Ⅴ Root SystemsCHAPTER Ⅵ Irreducible Characters and WeightsBibliographySymbol IndexSubject Index

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