Holomorphy and Convexity in Lie Theory

Karl-Hermann Neeb

Published by De Gruyter 2000

Holomorphy and Convexity in Lie Theory

Karl-Hermann Neeb

Volume 28 in the series De Gruyter Expositions in Mathematics

https://doi.org/10.1515/9783110808148

Overview
Contents

Reviews

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

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
A. Abstract Representation Theory
Chapter I. Reproducing Kernel Spaces Requires Authentication Unlicensed Licensed Download PDF	3
Chapter II. Representations of Involutive Semigroups Requires Authentication Unlicensed Licensed Download PDF	20
Chapter III. Positive Definite Functions on Involutive Semigroups Requires Authentication Unlicensed Licensed Download PDF	52
Chapter IV. Continuous and Holomorphic Representations Requires Authentication Unlicensed Licensed Download PDF	99
B. Convex Geometry and Representations of Vector Spaces
Chapter V. Convex Sets and Convex Functions Requires Authentication Unlicensed Licensed Download PDF	125
Chapter VI. Representations of Cones and Tubes Requires Authentication Unlicensed Licensed Download PDF	184
C. Convex Geometry of Lie Algebras
Chapter VII. Convexity in Lie Algebras Requires Authentication Unlicensed Licensed Download PDF	221
Chapter VIII. Convexity Theorems and Their Applications Requires Authentication Unlicensed Licensed Download PDF	265
D. Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups
Chapter IX. Unitary Highest Weight Representations: Algebraic Theory Requires Authentication Unlicensed Licensed Download PDF	327
Chapter X. Unitary Highest Weight Representations: Analytic Theory Requires Authentication Unlicensed Licensed Download PDF	387
Chapter XI. Complex Ol’shanskiĭ Semigroups and Their Representations Requires Authentication Unlicensed Licensed Download PDF	442
Chapter XII. Realization of Highest Weight Representations on Complex Domains Requires Authentication Unlicensed Licensed Download PDF	493
E. Complex Geometry and Representation Theory
Chapter XIII. Complex and Convex Geometry of Complex Semigroups Requires Authentication Unlicensed Licensed Download PDF	557
Chapter XIV. Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups Requires Authentication Unlicensed Licensed Download PDF	600
Chapter XV. Coherent State Representations Requires Authentication Unlicensed Licensed Download PDF	645
Appendices
Appendix I. Bounded Operators on Hilbert Spaces Requires Authentication Unlicensed Licensed Download PDF	665
Appendix II. Spectral Measures and Unbounded Operators Requires Authentication Unlicensed Licensed Download PDF	677
Appendix III. Holomorphic Functions on Infinite-Dimensional Spaces Requires Authentication Unlicensed Licensed Download PDF	686
Appendix IV. Symplectic Geometry Requires Authentication Unlicensed Licensed Download PDF	694
Appendix V. Simple Modules of p-Length 2 Requires Authentication Unlicensed Licensed Download PDF	705
Appendix VI. Symplectic Modules of Convex Type Requires Authentication Unlicensed Licensed Download PDF	715
Appendix VII. Square Integrable Representations of Locally Compact Groups Requires Authentication Unlicensed Licensed Download PDF	727
Appendix VIII. The Stone – von Neumann-Mackey Theorem Requires Authentication Unlicensed Licensed Download PDF	742
Bibliography Requires Authentication Unlicensed Licensed Download PDF	751
List of Symbols Requires Authentication Unlicensed Licensed Download PDF	767
Index Requires Authentication Unlicensed Licensed Download PDF	771

Language: English
Publisher: De Gruyter
Edition: Reprint 2011
Pages
- Front matter: 21
- Main content: 778
Illustrations
- Other: Num. figs.
Keywords: Unitäre Darstellung; Lie-Algebra; Holomorphe Darstellung

eBook

Published: April 20, 2011
ISBN: 9783110808148

Hardcover

Published: November 19, 1999
ISBN: 9783110156690