Preface |
Introduction |
Abstract Representation Theory / A.: |
Reproducing Kernel Spaces / Chapter I.: |
Operator-Valued Positive Definite Kernels / I.1.: |
The Cone of Positive Definite Kernels / I.2.: |
Representations of Involutive Semigroups / Chapter II.: |
Involutive Semigroups / II.1.: |
Bounded Representations / II.2.: |
Hermitian Representations / II.3.: |
Representations on Reproducing Kernel Spaces / II.4.: |
Positive Definite Functions on Involutive Semigroups / Chapter III.: |
Positive Definite Functions--the Discrete Case / III.1.: |
Enveloping C*-algebras / III.2.: |
Multiplicity Free Representations / III.3.: |
Continuous and Holomorphic Representations / Chapter IV.: |
Continuous Representations and Positive Definite Functions / IV.1.: |
Holomorphic Representations of Involutive Semigroups / IV.2.: |
Convex Geometry and Representations of Vector Spaces / B.: |
Convex Sets and Convex Functions / Chapter V.: |
Convex Sets and Cones / V.1.: |
Finite Reflection Groups and Convex Sets / V.2.: |
Convex Functions and Fenchel Duality / V.3.: |
Laplace Transforms / V.4.: |
The Characteristic Function of a Convex Set / V.5.: |
Representations of Cones and Tubes / Chapter VI.: |
Commutative Representation Theory / VI.1.: |
Representations of Cones / VI.2.: |
Holomorphic Representations of Tubes / VI.3.: |
Realization of Cyclic Representations by Holomorphic Functions / VI.4.: |
Holomorphic Extensions of Unitary Representations / VI.5.: |
Convex Geometry of Lie Algebras / C.: |
Convexity in Lie Algebras / Chapter VII.: |
Compactly Embedded Cartan Subalgebras / VII.1.: |
Root Decompositions / VII.2.: |
Lie Algebras With Many Invariant Convex Sets / VII.3.: |
Convexity Theorems and Their Applications / Chapter VIII.: |
Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.: |
The Structure of Admissible Lie Algebras / VIII.2.: |
Invariant Elliptic Cones in Lie Algebras / VIII.3.: |
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.: |
Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.: |
Generalized Highest Weight Representations / IX.1.: |
Positive Complex Polarizations / IX.2.: |
Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.: |
The Metaplectic Factorization / IX.4.: |
Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.: |
Unitary Highest Weight Representations: Analytic Theory / Chapter X.: |
The Convex Moment Set of a Unitary Representation / X.1.: |
Irreducible Unitary Representations / X.2.: |
The Metaplectic Representation and Its Applications / X.3.: |
Special Properties of Unitary Highest Weight Representations / X.4.: |
Moment Sets for C*-algebras / X.5.: |
Moment Sets for Group Representations / X.6.: |
Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.: |
Lawson's Theorem on Ol'shanskii Semigroups / XI.1.: |
Holomorphic Extension of Unitary Representations / XI.2.: |
Holomorphic Representations of Ol'shanskii Semigroups / XI.3.: |
Irreducible Holomorphic Representations / XI.4.: |
Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.: |
Decomposition and Characters of Holomorphic Representations / XI.6.: |
Realization of Highest Weight Representations on Complex Domains / Chapter XII.: |
The Structure of Groups of Harish-Chandra Type / XII.1.: |
Representations of Groups of Harish-Chandra Type / XII.2.: |
The Compression Semigroup and Its Representations / XII.3.: |
Examples / XII.4.: |
Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.: |
Complex Geometry and Representation Theory / E.: |
Complex and Convex Geometry of Complex Semigroups / Chapter XIII.: |
Locally Convex Functions and Local Recession Cones / XIII.1.: |
Invariant Convex Sets and Functions in Lie Algebras / XIII.2.: |
Calculations in Low-Dimensional Cases / XIII.3.: |
Biinvariant Plurisubharmonic Functions / XIII.4.: |
Complex Semigroups and Stein Manifolds / XIII.5.: |
Biinvariant Domains of Holomorphy / XIII.6.: |
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.: |
Biinvariant Hilbert Spaces / XIV.1.: |
Hardy Spaces Defined by Sup-Norms / XIV.2.: |
Hardy Spaces Defined by Square Integrability / XIV.3.: |
The Fine Structure of Hardy Spaces / XIV.4.: |
Coherent State Representations / Chapter XV.: |
Complex Structures on Homogeneous Spaces / XV.1.: |
Heisenberg's Uncertainty Principle and Coherent States / XV.2.: |
Appendices |
Bounded Operators on Hilbert Spaces / Appendix I.: |
Spectral Measures and Unbounded Operators / Appendix II.: |
Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.: |
Symplectic Geometry / Appendix IV.: |
Simple Modules of p-Length 2 / Appendix V.: |
Symplectic Modules of Convex Type / Appendix VI.: |
Square Integrable Representations of Locally Compact Groups / Appendix VII.: |
The Stone-von Neumann-Mackey Theorem / Appendix VIII.: |
Bibliography |
List of Symbols |
Index |
Preface |
Introduction |
Abstract Representation Theory / A.: |