Convexity properties of the coadjoint action of non-compact Lie groups
We call a coadjoint orbit of a finite dimensional real Lie algebra \({\mathfrak g}\) admissible if it is closed and its convex hull contains no affine lines. In this paper we study the closure of the set \({\mathfrak g}^*_{\text{adm}}\) of admissible coadjoint orbits in the dual \({\mathfrak g}^*\) of the Lie algebra \({\mathfrak g}\). In particular, we classify all orbits in this set which turns out to be a finite union of closed convex cones and show that the convex hull of an admissible orbit is always closed. We also use the results on coadjoint orbits to derive a new conjugacy theorem on adjoint orbits lying in convex cones.
scientific article; zbMATH DE number 1121715