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Russian–German conference on Several Complex Variables
March 2, 2012 11:30, Moscow, Steklov Mathematical Institute

The convex hull of compact adjoint orbits

Peter Heinzner

Ruhr-Universität Bochum
 Video records: Flash Video 320.2 Mb Flash Video 1,946.8 Mb MP4 320.2 Mb

Abstract: The Satake–Furstenberg compactification of a real symmetric space of non-compact type is closely related to the convex hull $\hat{\mathrm O}$ of a $K$-orbit $\mathrm O$ in $\mathfrak p$, where $\mathfrak g=\mathfrak k+\mathfrak p$ denotes a Cartan decomposition of the Lie algebra of a semisimple Lie group $G$. In this talk we give a precise description of $\hat{\mathrm{O}}$ in terms of the geometry of $\mathrm O$ given by compact orbits of minimal parabolic subgroups of $G$ in $\mathrm O$.