Root polytopes and growth series of root lattices

Details Root polytopes and growth series of root lattices Root polytopes and growth series of root lattices

2008-09-30

arxiv.org/abs/0809.5123v1

Mathematics

Combinatorics

17 pages, 3 figures

Scientific paper

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 A_n, C_n, and D_n, 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.

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