Root Polytopes and Growth Series of Root Lattices

The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root lattices An, Cn and Dn, and compute their f-and h-vectors. This leads us to recover formulae for the growth series of these root lattices, which were first conjectured by Conway–Mallows–Sloane and Baake–Grimm and proved by Conway–Sloane and Bacher–de la Harpe–Venkov.

• Type: Journal
• Year: 2011
• Where: SIAMDM
• Authors: Federico Ardila, Matthias Beck, Serkan Hosten, Julian Pfeifle, Kim Seashore
• Keywords: Classical Root Lattice, Explicit Unimodular Triangulations, Root Lattices, SIAMDM 2011, Software Engineering