Convex Geometry of co-adjoint orbits and convex hulls

Date/heure
16 mars 2015
14:00 - 15:00

Oratrice ou orateur
Peter Heinzner

Catégorie d'évènement
Séminaire de géométrie complexe

Coadjoint orbits of Lie groups are examples of symplectic manifolds endowed
with a Hamiltonian action. We will consider elliptic coadjoint orbits
of a real semi-simple Lie group $G$. If $G$ is a compact Lie group, then any
orbit $O$ is elliptic. In the general setup the orbit $O$ has a unique invariant
complex structure such that the Kirillov-Kostant-Souriau form is Kählerian.
It turns out that the convex hull $hatO$ of $O$ is closely related to the complex
geometry of $O$. More precisely, the faces of $hatO$ are given as convex hulls of
orbits of centralizer subgroups and there is a strong connection to compact
orbits of parabolic subgroups of the complexi ed group $G^{mathbbC}$.