$C^{\infty}$-vectors of irreducible representations of exponential solvable Lie groups

Irreducible Representations of Solvable Lie Superalgebras

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V. Kac is refined. In reality these representations are not just induced from a polarization but are twisted ones, as infinite dimensional representations of solvable Lie algebras. Various cases of irreducibility (general and of type Q) are classified.

Quantization and Representations of Solvable Lie Groups

Introduction. In this note, we will announce a characterization of a connected, simply connected Type I solvable Lie group, G, and present a complete description of the set of all unitary equivalence classes of irreducible unitary representations of G together with a construction of an irreducible representation in each equivalence class. This result subsumes the results previously obtained on ...

Classification of the irreducible representations of semisimple Lie groups.

We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G, in terms of their restriction to a maximal compact subgroup K of G. (A classification in terms of analytic properties of the representations has been given by R. P. Langlands [(1973), mimeographed notes, Institute for Advanced Study, Princeton, NJ] for linear groups.) We first defin...

Classification of irreducible tempered representations of semisimple Lie groups.

For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langland's classification of all irreducible admissible representations for such groups. Since no...

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras