Harmonic Analysis on Semi-Simple Lie Groups I

Content: 1 The Structure of Real Semi-Simple Lie Groups --
1.1 Preliminaries --
1.2 The Bruhat Decomposition --
Parabolic 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 --
Generalities --
2.2 Invariant Theory II --
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.