%0 Journal Article
%T Orbitopes
%A Raman Sanyal
%A Frank Sottile
%A Bernd Sturmfels
%J Mathematics
%D 2009
%I arXiv
%R 10.1112/S002557931100132X
%X An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector space. These highly symmetric convex bodies lie at the crossroads of several fields, in particular convex geometry, optimization, and algebraic geometry. We present a self-contained theory of orbitopes, with particular emphasis on instances arising from the groups SO(n) and O(n). These include Schur-Horn orbitopes, tautological orbitopes, Caratheodory orbitopes, Veronese orbitopes and Grassmann orbitopes. We study their face lattices, their algebraic boundary hypersurfaces, and representations as spectrahedra or projected spectrahedra.
%U http://arxiv.org/abs/0911.5436v4