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Representation Theory of Semisimple Groups : an overview based on examples, with a new preface by the author /
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 rese...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey
Princeton University Press,
2016.
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| Colección: | Princeton mathematical series.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Knapp, Anthony W. | |
| 245 | 1 | 0 | |a Representation Theory of Semisimple Groups : |b an overview based on examples, with a new preface by the author / |c Anthony W. Knapp |
| 260 | |a New Jersey |b Princeton University Press, |c 2016. | ||
| 300 | |a 1 online resource (xix, 774 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Princeton Mathematical Series ; |v v. Vol. 36 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title; Copyright; Dedication; Contents; PREFACE TO THE PRINCETON LANDMARKS IN MATHEMATICS EDITION; PREFACE; ACKNOWLEDGMENTS; CHAPTER I. 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 II. REPRESENTATIONS OF SU(2), SL(2, R), AND SL(2, C); 1. The Unitary Trick; 2. Irreducible Finite-Dimensional Complex-Linear Representations of sl(2, C) | |
| 505 | 8 | |a 3. Finite-Dimensional Representations of sl(2, C)4. Irreducible Unitary Representations of SL(2, C); 5. Irreducible Unitary Representations of SL(2, R); 6. Use of SU(1,1); 7. Plancherel Formula; 8. Problems; CHAPTER III. C^∞ VECTORS AND THE UNIVERSAL ENVELOPING ALGEBRA; 1. Universal Enveloping Algebra; 2. Actions on Universal Enveloping Algebra; 3. C^∞ Vectors; 4. Gårding Subspace; 5. Problems; CHAPTER IV. REPRESENTATIONS OF COMPACT LIE GROUPS ; 1. Examples of Root Space Decompositions; 2. Roots; 3. Abstract Root Systems and Positivity; 4. Weyl Group, Algebraically | |
| 505 | 8 | |a 5. Weights and Integral Forms6. Centalizers of Tori; 7. Theorem of the Highest Weight; 8. Verma Modules; 9. Weyl Group, Analytically; 10. Weyl Character Formula; 11. Problems; CHAPTER V. 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 VI. HOLOMORPHIC DISCRETE SERIES ; 1. Holomorphic Discrete Series for SU(1,1) | |
| 505 | 8 | |a 2. Classical Bounded Symmetric Domains3. Harish-Chandra Decomposition; 4. Holomorphic Discrete Series; 5. Finiteness of an Integral; 6. Problems; CHAPTER VII. INDUCED REPRESENTATIONS; 1. Three Pictures; 2. Elementary Properties; 3. Bruhat Theory; 4. Formal Intertwining Operators; 5. Gindikin-Karpelevič 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 H function; 10. Estimates on Intertwining Operators, Part II | |
| 505 | 8 | |a 11. Tempered Representations and Langlands Quotients12. Problems; CHAPTER VIII. ADMISSIBLE REPRESENTATIONS ; 1. Motivation; 2. Admissible Representations; 3. Invariant Subspaces; 4. Framework for Studying Matrix Coefficients; 5. Harish-Chandra Homomorphism; 6. Infinitesimal Character; 7. Differential Equations Satisfied by Matrix Coefficients; 8. Asymptotic Expansions and Leading Exponents; 9. First Application: Subrepresentation Theorem; 10. Second Application: Analytic Continuation of Interwining Operators, Part II | |
| 520 | |a 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. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Semisimple Lie groups. | |
| 650 | 0 | |a Representations of groups. | |
| 650 | 4 | |a Semisimple lie groups. | |
| 650 | 6 | |a Groupes de Lie semi-simples. | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 650 | 7 | |a Semisimple Lie groups |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Knapp, Anthony W. |t Representation Theory of Semisimple Groups : An Overview Based on Examples (PMS-36). |d Princeton : Princeton University Press, ©2016 |z 9780691090894 |
| 830 | 0 | |a Princeton mathematical series. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt1bpm9sn |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL4510789 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis34537682 | ||
| 938 | |a YBP Library Services |b YANK |n 12979703 | ||
| 994 | |a 92 |b IZTAP | ||