Groupes et algèbres de Lie

Abstract: . We determine the Lie algebras of all simply transitive groups of automorphisms of a homogeneous Siegel domain D as modifications of standard normal j-algebras. We show that the Lie algebra of all automorphisms of D is a "complete isometry algebra in standard position". This implies that D carries a riemannian metric g with nonpositive sectional curvature satisfying Lie Iso(D, g) = Lie Aut D. We determine all Kahler metrics f on D for which the group Aut(£>, /) of holomorphic isometries acts transitively. We prove that in this case Aut(D, f) contains a simply transitive split solvable subgroup. The results of this paper are used to prove the fundamental conjecture for homogeneous Kahler manifolds admitting a solvable transitive group of automorphisms.

TL;DR: In this article, the authors deal with Radon transforms for generalized flag manifolds in the framework of quasi-equivariant D -modules and give a sufficient condition in order that a D -module associated to an equivariant locally free O -module is transformed into an object of the same type.

TL;DR: In this paper, structural results on the Lie algebras of transitive isometry groups of a general compact homogenous Riemannian manifold with nontrivial Killing vector fields of constant length are presented.