內容簡介
《半單群的表示論(第2卷)》主要內容包括：SCOPEOFTHETHEORY、REPRESENTATIONSOFSU(2),SL(2,R),AND、CVECTORSANDTHEUNIVERSALENVELOPINGALGEBRA、REPRESENTATIONSOFCOMPACTLIEGROUPS、HOLOMORPHICDISCRETESERIES、INDUCEDREPRESENTATIONS、admissibleREPRESENTATIONS、CONSTRUCTIONOFDISCRETESERIES、GLOBALCHARACTERS、exhaustionOFDISCRETESERIES、PLANCHERELFORMULA、IRREDUCLBLETEMPEREDREPRESENTATIONS、MINIMALKTYPES、unitaryREPRESENTATIONS等。
作者簡介
作者：(美國)納普(AnthonyW.Knapp)
目錄
PREFACE TO THE PRINCETON LANDMARKS IN
MATHEMATICS EDITION
PREFACE
ACKNOWLEDGMENTS
CHAPTER 1 SCOPE OF THE THEORY
1. The Classical Groups
2. Cartan Decomposition
3. Representations
4. Concrete Problems in Representation Theory
5. Abstract Theory for Compact Groups
6. Application of the Abstract Theory to Lie Groups
7. Problems
CHAPTER 2 REPRESENTATIONS OF SU（2）, SL（2, R）, AND
SL（2, C）
1. The Unitary Trick
2. Irreducible Finite-Dimensional Complex-Linear
Representations of SI（2, C）
3. Finite-Dimensional Representations of SI（2, C）
4. Irredudble Unitary Representations of SL（2, C）
S. Irreducible Unitary Representations of SL（2, R）
6. Use of SU（1, 1）
7. Plancherel Formula
8. Problems
CHAPTER 3 C VECTORS AND THE UNIVERSAL ENVELOPING ALGEBRA
1. Universal Enveloping Algebra
2. Actions on Universal Enveloping Algebra
3. C Vectors
4. Garding Subspace
5. Problems
CHAPTER 4 REPRESENTATIONS OF COMPACT LIE GROUPS
1. Examples of Root Space Decompositions
2.roots
3. Abstract Root Systems and Positivity
4. Weyl Group, Algebraica11y
5. Weights and Integral Forms
6. Centalizers of Tori
7. Theorem of the Highest Weight
8. Verma Modules
9. Weyl Group, Analytica11y
10. Weyl Character Formula
11. Problems
CHAPTER 5 STRUCTURE THEORY FOR NONCOMPACT GROUPS
1. Cartan Decomposition and the Unitary Trick
2. Iwasawa Decomposition
3. Regular Elements, Weyl Chambers, and the Weyl Group
4. Other Decompositions
5. Parabolic Subgroups
6. Integral Formulas
7. Borel-Weil Theorem
8. Problems
CHAPTER 6 HOLOMORPHIC DISCRETE SERIES
1. Holomorphic Discrete Series for SU（1, 1）
2. Classical Bounded Symmetric Domains
3. Harish-chandraDecomposition
4. HOlomorphic Discrete Series
5. Finiteness of an Integral
6. Problems
CHAPTER 7 INDUCED REPRESENTATIONS
1. Three Pictures
2. Elementary Properties
3. Bruhat Theory
4. Formal Intertwining Operators
5. Gindikin-Karpelevic Formula
6. Estimates on Intertwining Operators, Part I
7. Analytic Continuation of Intertwining Operators,Part I
8. Spherical Functions
9. Finite-Dimensional Representations and the Hfunction
……
CHAPTER 8 ADMISSIBLE REPRESENTATIONS
CHAPTER 9 CONSTRUCTION OF DISCRETE SERIES
CHAPTER 10 GLOBAL CHARACTERS
CHAPTER 11 INTRODUCTION TO PLANCHEREL FORMULA
CHAPTER 12 EXHAUSTION OF DISCRETE SERIES
CHAPTER 13 PLANCHEREL FORMULA
CHAPTER 14 IRREDUCLBLE TEMPERED REPRESENTATIONS
CHAPTER 15 MINIMAL K TYPES
CHAPTER 16 UNITARY REPRESENTATIONS
APPENDIX A: ELEMENTARY THEORY OF LIE GROUPS
APPENDIX B:REGULAR SINGULAR POINTS OF PARTIAL DIFFERENTIAL EQUATIONS
APPENDIX C:ROOTS AND RESTRICTED ROOTS FOR CLASSICAL GROUPS
NOTES
REFERENCES
INDEX OF NOTATION
INDEX
