Representations of Solvable Lie Groups. Basic Theory and Examples

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Arnal D., Currey B., III. Representations of Solvable Lie Groups Series Title Copyright Contents Preface 1 Basic theory of solvable Lie algebras and Lie groups 1.1 Solvable Lie algebras 1.2 Representations of a Lie algebra and weights 1.3 The Lie theorem and its first consequences 1.4 Adjoint and coadjoint representations 1.5 Ado theorem for a solvable Lie algebra 1.6 Lie groups 1.7 Nilpotent and solvable Lie groups 1.8 Exponential groups 1.9 Finite-dimensional group representations 2 Stratification of an orbit space 2.1 Matrix normal form 2.2 Layers for a representation 2.3 Orbit structure for a completely solvable action 2.4 Construction of rational supplementary elements 2.5 Orbit structure for an action of exponential type 2.6 Structure of the generic layer 3 Unitary representations 3.1 Unitary representations 3.2 Decomposition of representations 3.3 Induced representations 3.4 Elements of Mackey theory 4 Coadjoint orbits and polarizations 4.1 Coadjoint orbits 4.2 Polarizations 4.3 Admissibility and the Pukanszky condition 4.4 Isotropic subspaces associated to a flag 4.5 Fine layering and Vergne polarizations 4.6 Positivity and properties of polarizations 4.7 Integral orbits 5 Irreducible unitary representations 5.1 Holomorphic induction 5.2 Construction of irreducible representations 5.3 Orbit method for solvable groups 6 Plancherel formula and related topics 6.1 Invariant measure on a coadjoint orbit 6.2 Character formula 6.3 Semicharacters and the Plancherel formula List of notations Bibliography Index