Faces of root polytopes

Abstract

We completely characterize the faces of the root polytope ${\tilde{Q}}_G=\text{conv}\{0,{\mathbf{e}}_i-{\mathbf{e}}_j(i,j)\in E(G)\}$ combinatorially. Our results specialize to state of the art results in a straightforward way.

arXiv comment18 pages, 8 figures. v2: corrected proof of lemma 3.19