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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Knapp, Anthony W.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New Jersey Princeton University Press, 2016.
Colección:Princeton mathematical series.
Temas:
Semisimple Lie groups.
Representations of groups.
Semisimple lie groups.
Groupes de Lie semi-simples.
Représentations de groupes.
Representations of groups
Semisimple Lie groups
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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)
  • 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
  • 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)
  • 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
  • 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

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