A combinatorial description of stability for toric vector bundles

Abstract: The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric vector bundles by Di Rocco, Jabbusch and Smith. We also define subparliaments of polytopes and identify them with parliaments of equivariant subbundles.