Holomorphy and convexity in Lie theory /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Neeb, Karl-Hermann
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Walter de Gruyter, 2000.
Colección:De Gruyter expositions in mathematics ; 28.
Temas:
Lie groups.
Representations of groups.
Convex functions.
Groupes de Lie.
Représentations de groupes.
Fonctions convexes.
MATHEMATICS > Algebra > Intermediate.
Lie-algebra's.
Holomorfe functies.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • A. Abstract Representation Theory
  • Chapter I. Reproducing Kernel Spaces 3
  • I.1. Operator-Valued Positive Definite Kernels 3
  • I.2. The Cone of Positive Definite Kernels 14
  • Chapter II. Representations of Involutive Semigroups 20
  • II. 1. Involutive Semigroups 21
  • II. 2. Bounded Representations 24
  • II. 3. Hermitian Representations 29
  • II. 4. Representations on Reproducing Kernel Spaces 34
  • Chapter III. Positive Definite Functions on Involutive Semigroups 52
  • III. 1. Positive Definite Functions
  • the Discrete Case 53
  • III. 2. Enveloping C*-algebras 68
  • III. 3. Multiplicity Free Representations 80
  • Chapter IV. Continuous and Holomorphic Representations 99
  • IV. 1. Continuous Representations and Positive Definite Functions 99
  • IV. 2. Holomorphic Representations of Involutive Semigroups 119
  • B. Convex Geometry and Representations of Vector Spaces
  • Chapter V. Convex Sets and Convex Functions 125
  • V.1. Convex Sets and Cones 126
  • V.2. Finite Reflection Groups and Convex Sets 138
  • V.3. Convex Functions and Fenchel Duality 147
  • V.4. Laplace Transforms 163
  • V.5. The Characteristic Function of a Convex Set 174
  • Chapter VI. Representations of Cones and Tubes 184
  • VI. 1. Commutative Representation Theory 185
  • VI. 2. Representations of Cones 195
  • VI. 3. Holomorphic Representations of Tubes 205
  • VI. 4. Realization of Cyclic Representations by Holomorphic Functions 209
  • VI. 5. Holomorphic Extensions of Unitary Representations 214
  • C. Convex Geometry of Lie Algebras
  • Chapter VII. Convexity in Lie Algebras 221
  • VII. 1. Compactly Embedded Cartan Subalgebras 222
  • VII. 2. Root Decompositions 231
  • VII. 3. Lie Algebras With Many Invariant Convex Sets 251
  • Chapter VIII. Convexity Theorems and Their Applications 265
  • VIII. 1. Admissible Coadjoint Orbits and Convexity Theorems 266
  • VIII. 2. The Structure of Admissible Lie Algebras 292
  • VIII. 3. Invariant Elliptic Cones in Lie Algebras 306
  • D. Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups
  • Chapter IX. Unitary Highest Weight Representations: Algebraic Theory 327
  • IX. 1. Generalized Highest Weight Representations 328
  • IX. 2. Positive Complex Polarizations 344
  • IX. 3. Highest Weight Modules of Finite-Dimensional Lie Algebras 356
  • IX. 4. The Metaplectic Factorization 361
  • IX. 5. Unitary Highest Weight Representations of Hermitian Lie Algebras 374
  • Chapter X. Unitary Highest Weight Representations: Analytic Theory 387
  • X.1. The Convex Moment Set of a Unitary Representation 388
  • X.2. Irreducible Unitary Representations 394
  • X.3. The Metaplectic Representation and Its Applications 400
  • X.4. Special Properties of Unitary Highest Weight Representations 411
  • X.5. Moment Sets for C*-algebras 419
  • X.6. Moment Sets for Group Representations 428
  • Chapter XI. Complex Ol'shanskii Semigroups and Their Representations 442
  • XI. 1. Lawson's Theorem on Ol'shanskii Semigroups 443
  • XI. 2. Holomorphic Extension of Unitary Representations 457
  • XI. 3. Holomorphic Representations of Ol'shanskii Semigroups 464
  • XI. 4. Irreducible Holomorphic Representations 470
  • XI. 5. Gelfand-Raikov Theorems for Ol'shanskii Semigroups 476
  • XI. 6. Decomposition and Characters of Holomorphic Representations 477
  • Chapter XII. Realization of Highest Weight Representations on Complex Domains 493
  • XII. 1. The Structure of Groups of Harish-Chandra Type 494
  • XII. 2. Representations of Groups of Harish-Chandra Type 514
  • XII. 3. The Compression Semigroup and Its Representations 524
  • XII. 5. Hilbert Spaces of Square Integrable Holomorphic Functions 538
  • E. Complex Geometry and Representation Theory
  • Chapter XIII. Complex and Convex Geometry of Complex Semigroups 557
  • XIII. 1. Locally Convex Functions and Local Recession Cones 559
  • XIII. 2. Invariant Convex Sets and Functions in Lie Algebras 563
  • XIII. 3. Calculations in Low-Dimensional Cases 571
  • XIII. 4. Biinvariant Plurisubharmonic Functions 576
  • XIII. 5. Complex Semigroups and Stein Manifolds 586
  • XIII. 6. Biinvariant Domains of Holomorphy 595
  • Chapter XIV. Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups 600
  • XIV. 1. Biinvariant Hilbert Spaces 601
  • XIV. 2. Hardy Spaces Defined by Sup-Norms 608
  • XIV. 3. Hardy Spaces Defined by Square Integrability 616
  • XIV. 4. The Fine Structure of Hardy Spaces 623
  • Chapter XV. Coherent State Representations 645
  • XV. 1. Complex Structures on Homogeneous Spaces 646
  • XV. 2. Coherent State Representations 650
  • XV. 3. Heisenberg's Uncertainty Principle and Coherent States 656
  • Appendix I. Bounded Operators on Hilbert Spaces 665
  • Appendix II. Spectral Measures and Unbounded Operators 677
  • Appendix III. Holomorphic Functions on Infinite-Dimensional Spaces 686
  • Appendix IV. Symplectic Geometry 694
  • Appendix V. Simple Modules of p-Length 2 705
  • Appendix VI. Symplectic Modules of Convex Type 715
  • Appendix VII. Square Integrable Representations of Locally Compact Groups 727
  • Appendix VIII. The Stone-von Neumann-Mackey Theorem 742.

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