Orbitopes

Abstract

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.

37 pages. minor revisions of original

References in corpus (5)

• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
• Edges of the Barvinok-Novik orbitope
• Dimensional Differences between Nonnegative Polynomials and Sums of Squares
• Matrix Cubes Parametrized by Eigenvalues

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