Author | Warner, Garth. author |
---|---|
Title | Harmonic Analysis on Semi-Simple Lie Groups I [electronic resource] / by Garth Warner |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1972 |
Connect to | http://dx.doi.org/10.1007/978-3-642-50275-0 |
Descript | XVI, 532 p. 2 illus. online resource |
1 The Structure of Real Semi-Simple Lie Groups -- 1.1 Preliminaries -- 1.2 The Bruhat DecompositionโParabolic Subgroups -- 1.3 Cartan Subalgebras -- 1.4 Cartan Subgroups -- 2 The Universal Enveloping Algebra of a Semi-Simple Lie Algebra -- 2.1 Invariant Theory I โ Generalities -- 2.2 Invariant Theory II โ Applications to Reductive Lie Algebras -- 2.3 On the Structure of the Universal Enveloping Algebra -- 2.4 Representations of a Reductive Lie Algebra -- 2.5 Representations on Cohomology Groups -- 3 Finite Dimensional Representations of a Semi-Simple Lie Group -- 3.1 Holomorphic Representations of a Complex Semi-Simple Lie Group -- 3.2 Unitary Representations of a Compact Semi-Simple Lie Group -- 3.3 Finite Dimensional Class One Representations of a Real Semi-Simple Lie Group -- 4 Infinite Dimensional Group Representation Theory -- 4.1 Representations on a Locally Convex Space -- 4.2 Representations on a Banach Space -- 4.3 Representations on a Hubert Space -- 4.3.1 Generalities -- 4.3.2 Examples -- 4.4 Differentiable Vectors, Analytic Vectors -- 4.5 Large Compact Subgroups -- 5 Induced Representations -- 5.1 Unitarily Induced Representations -- 5.2 Quasi-Invariant Distributions -- 5.3 Irreducibility of Unitarily Induced Representations -- 5.4 Systems of Imprimitivity -- 5.5 Applications to Semi-Simple Lie Groups -- Appendices -- 1 Quasi-Invariant Measures -- 2 Distributions on a Manifold -- 2.1 Differential Operators and Function Spaces -- 2.2 Tensor Products of Topological Vector Spaces -- 2.3 Vector Distributions -- 2.4 Distributions on a Lie Group -- General Notational Conventions -- List of Notations -- Guide to the Literature