Representation Theory of Semisimple Groups

"Each [theme] is developed carefully and thoroughly, with beautifully worked examples and proofs that reflect long experience in teaching and research. . . . This result is delightful: a readable text that loses almost none of its value as a reference work."---David A. Vogan Jr., Bulletin of the American Mathematical Society

Autorentext
Anthony W. Knapp With a new preface by the author

Klappentext
In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and researchers. Although theorems are always stated precisely, many illustrative examples or classes of examples are given. To support this unique approach, the author includes for the reader a useful 300-item bibliography and an extensive section of notes.

Zusammenfassung
Offers a survey of representation theory of semisimple Lie groups. Suitable for both graduate students and researchers, this book states the theorems precisely, and gives many illustrative examples or classes of examples. It includes for the reader a useful 300-item bibliography and an extensive section of notes.

Inhalt
Preface to the Princeton Landmarks in Mathematics Edition xiii
Preface xv
Acknowledgments xix CHAPTER I. SCOPE OF THE THEORY
1. The Classical Groups 3
2. Cartan Decomposition 7
3. Representations 10
4. Concrete Problems in Representation Theory 14
5. Abstract Theory for Compact Groups 14
6. Application of the Abstract Theory to Lie Groups 23
7. Problems 24 CHAPTER II. REPRESENTATIONS OF SU(2), SL(2,R), AND SL(2,C)
l. The Unitary Trick 28
2. Irreducible Finite-Dimensional Complex-Linear Representations of 91(2,C) 30
3. Finite-Dimensional Representations of 91(2,C) 31
4. Irreducible Unitary Representations of SL(2,C) 33
5. Irreducible Unitary Representations of SL(2,08) 35
6. Use of SU(1,1) 39
7. Plancherel Formula 41
8. Problems 42 CHAPTER III. C VECTORS AND THE UNIVERSAL ENVELOPING ALGEBRA
l. Universal Enveloping Algebra 46
2. Actions on Universal Enveloping Algebra 50
3. C Vectors 55
4. Garding Subspace. Problems 57 CHAPTER IV. REPRESENTATIONS OF COMPACT LIE GROUPS
1. Examples of Root Space Decompositions 60
2. Roots 65
3. Abstract Root Systems and Positivity 72
4. Weyl Group, Algebraically 78
5. Weights and Integral Forms 81
6. Centalizers of Tori 86
7. Theorem of the Highest Weight 89
8. Verma Modules 93
9. Weyl Group, Analytically 100
10. Weyl Character Formula 104
11. Problems 109 CHAPTER V. STRUCTURE THEORY FOR NONCOMPACT GROUPS
l. Cartan Decomposition and the Unitary Trick 113
2. Iwasawa Decomposition 116
3. Regular Elements, Weyl Chambers, and the Weyl Group 121
4. Other Decompositions 126
5. Parabolic Subgroups 132
6. Integral Formulas 137
7. Borel-Weil Theorem 142
8. Problems 147 CHAPTER VI. HOLOMORPHIC DISCRETE SERIES
1. Holomorphic Discrete Series for SU(1,1) 150
2. Classical Bounded Symmetric Domains 152
3. Harish-Chandra Decomposition 153
4. Holomorphic Discrete Series 158
5. Finiteness of an Integral 161
6. Problems 164 CHAPTER VII. INDUCED REPRESENTATIONS
1. Three Pictures 167
2. Elementary Properties 169
3. Bruhat Theory 172
4. Formal Intertwining Operators 174
5. Gindikin-Karpelevic Formula 177
6. Estimates on Intertwining Operators, Part I 181
7. Analytic Continuation of Intertwining Operators, Part I 183
8. Spherical Functions 185
9. Finite-Dimensional Representations and the H function 191
10. Estimates on Intertwining Operators, Part II 196
11. Tempered Representations and Langlands Quotients 198
12. Problems 201 CHAPTER VIII. ADMISSIBLE REPRESENTATIONS
l. Motivation 203
2. Admissible Representations 205
3. Invariant Subspaces 209
4. Framework for Studying Matrix Coefficients 215
5. Harish-Chandra Homomorphism 218
6. Infinitesimal Character 223
7. Differential Equations Satisfied by Matrix Coefficients 226
8. Asymptotic Expansions and Leading Exponents 234
9. First Application: Subrepresentation Theorem 238
10. Second Application: Analytic Continuation of Interwining Operators, Part II 239
11. Third Application: Control of K-Finite Z(gc)-Finite Functions 242
12. Asymptotic Expansions near the Walls 247
13. Fourth Application: Asymptotic Size of Matrix Coefficients 253
14. Fifth Application: Identification of Irreducible Tempered Representations 258
15. Sixth Application: Langlands Classification of Irreducible Admissible Representations 266
16. Problems 276 CHAPTER IX. CONSTRUCTION OF DISCR

#	Onlineshop	Preis CHF	Versand CHF	Total CHF
1	Seller	0.00	0.00	0.00