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Holomorphy and Convexity in Lie Theory : de Gruyter Expositions in Mathematics - Karl-Hermann Neeb

Holomorphy and Convexity in Lie Theory

de Gruyter Expositions in Mathematics

Hardcover Published: 1st January 2000
ISBN: 9783110156690
Number Of Pages: 799
For Ages: 22+ years old

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Industry Reviews

"This monograph is a remarkable collection of facts, theorems and theories concerning such subjects as holomorphy and convexity in Lie theory." Zentralblatt fur Mathematik

Prefacep. v
Introductionp. xiii
Abstract Representation Theory
Reproducing Kernel Spacesp. 3
Operator-Valued Positive Definite Kernelsp. 3
The Cone of Positive Definite Kernelsp. 14
Representations of Involutive Semigroupsp. 20
Involutive Semigroupsp. 21
Bounded Representationsp. 24
Hermitian Representationsp. 29
Representations on Reproducing Kernel Spacesp. 34
Positive Definite Functions on Involutive Semigroupsp. 52
Positive Definite Functions--the Discrete Casep. 53
Enveloping C*-algebrasp. 68
Multiplicity Free Representationsp. 80
Continuous and Holomorphic Representationsp. 99
Continuous Representations and Positive Definite Functionsp. 99
Holomorphic Representations of Involutive Semigroupsp. 119
Convex Geometry and Representations of Vector Spaces
Convex Sets and Convex Functionsp. 125
Convex Sets and Conesp. 126
Finite Reflection Groups and Convex Setsp. 138
Convex Functions and Fenchel Dualityp. 147
Laplace Transformsp. 163
The Characteristic Function of a Convex Setp. 174
Representations of Cones and Tubesp. 184
Commutative Representation Theoryp. 185
Representations of Conesp. 195
Holomorphic Representations of Tubesp. 205
Realization of Cyclic Representations by Holomorphic Functionsp. 209
Holomorphic Extensions of Unitary Representationsp. 214
Convex Geometry of Lie Algebras
Convexity in Lie Algebrasp. 221
Compactly Embedded Cartan Subalgebrasp. 222
Root Decompositionsp. 231
Lie Algebras With Many Invariant Convex Setsp. 251
Convexity Theorems and Their Applicationsp. 265
Admissible Coadjoint Orbits and Convexity Theoremsp. 266
The Structure of Admissible Lie Algebrasp. 292
Invariant Elliptic Cones in Lie Algebrasp. 306
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups
Unitary Highest Weight Representations: Algebraic Theoryp. 327
Generalized Highest Weight Representationsp. 328
Positive Complex Polarizationsp. 344
Highest Weight Modules of Finite-Dimensional Lie Algebrasp. 356
The Metaplectic Factorizationp. 361
Unitary Highest Weight Representations of Hermitian Lie Algebrasp. 374
Unitary Highest Weight Representations: Analytic Theoryp. 387
The Convex Moment Set of a Unitary Representationp. 388
Irreducible Unitary Representationsp. 394
The Metaplectic Representation and Its Applicationsp. 400
Special Properties of Unitary Highest Weight Representationsp. 411
Moment Sets for C*-algebrasp. 419
Moment Sets for Group Representationsp. 428
Complex Ol'shanskii Semigroups and Their Representationsp. 442
Lawson's Theorem on Ol'shanskii Semigroupsp. 443
Holomorphic Extension of Unitary Representationsp. 457
Holomorphic Representations of Ol'shanskii Semigroupsp. 464
Irreducible Holomorphic Representationsp. 470
Gelfand-Raikov Theorems for Ol'shanskii Semigroupsp. 476
Decomposition and Characters of Holomorphic Representationsp. 477
Realization of Highest Weight Representations on Complex Domainsp. 493
The Structure of Groups of Harish-Chandra Typep. 494
Representations of Groups of Harish-Chandra Typep. 514
The Compression Semigroup and Its Representationsp. 524
Examplesp. 530
Hilbert Spaces of Square Integrable Holomorphic Functionsp. 538
Complex Geometry and Representation Theory
Complex and Convex Geometry of Complex Semigroupsp. 557
Locally Convex Functions and Local Recession Conesp. 559
Invariant Convex Sets and Functions in Lie Algebrasp. 563
Calculations in Low-Dimensional Casesp. 571
Biinvariant Plurisubharmonic Functionsp. 576
Complex Semigroups and Stein Manifoldsp. 586
Biinvariant Domains of Holomorphyp. 595
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroupsp. 600
Biinvariant Hilbert Spacesp. 601
Hardy Spaces Defined by Sup-Normsp. 608
Hardy Spaces Defined by Square Integrabilityp. 616
The Fine Structure of Hardy Spacesp. 623
Coherent State Representationsp. 645
Complex Structures on Homogeneous Spacesp. 646
Coherent State Representationsp. 650
Heisenberg's Uncertainty Principle and Coherent Statesp. 656
Appendices
Bounded Operators on Hilbert Spacesp. 665
Spectral Measures and Unbounded Operatorsp. 677
Holomorphic Functions on Infinite-Dimensional Spacesp. 686
Symplectic Geometryp. 694
Simple Modules of p-Length 2p. 705
Symplectic Modules of Convex Typep. 715
Square Integrable Representations of Locally Compact Groupsp. 727
The Stone-von Neumann-Mackey Theoremp. 742
Bibliographyp. 751
List of Symbolsp. 767
Indexp. 771
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9783110156690
ISBN-10: 3110156695
Series: de Gruyter Expositions in Mathematics
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 799
Published: 1st January 2000
Country of Publication: DE
Dimensions (cm): 24.54 x 18.06  x 4.83
Weight (kg): 1.42

Earn 362 Qantas Points
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