Generalized conformal structures on classical real Lie groups and related problems on the theory of representations. (English. Abridged French version) Zbl 0788.22008

The author defines the generalized conformal compactification of a classical real Lie group \(G\). Correspondingly the regular representation of \(G\) extends to a unitary representation of the generalized conformal group \(\widetilde G\supset G\times G\) with a finite number of irreducible components. For the conformal structure that the author defined there are analogs of some classical results. For instance there is an analog of the Liouville theorem saying that a local automorphism can be extended to a global one. Also this structure is flat. This fact is related to the parabolic affinization.
Reviewer: A.K.Guts (Omsk)


22E15 General properties and structure of real Lie groups
53C30 Differential geometry of homogeneous manifolds