《半單群的表示論》是由2011年世界圖書出版公司出版的圖書，作者是納普。本書分為上下兩卷，前十章為上卷，後六章為下卷。書中講述半單李群表示理論的方式給出了本科目的精華，符合學習的自然規律。
基本介紹
- 書名：半單群的表示論
- 又名： representation theory of semisimple groups vol.2
- ISBN：9787510029578, 7510029570
- 頁數：773頁
- 出版社：世界圖書出版公司
- 出版時間：2011年1月1日
- 開本：24
內容簡介,作者簡介,目錄,
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-Chandra Decomposition
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
