Triangulations of root polytopes
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 115-145.

Let Φ be an irreducible crystallographic root system and 𝒫 its root polytope, i.e., the convex hull of Φ. We provide a uniform construction, for all root types, of a triangulation of the facets of 𝒫. We also prove that, on each orbit of facets under the action of the Weyl group, the triangulation is unimodular with respect to a root sublattice that depends on the orbit.

Received: 2017-08-01
Revised: 2017-10-11
Accepted: 2017-10-13
Published online: 2018-01-29
DOI: https://doi.org/10.5802/alco.7
Classification: 17B20,  17B22,  20F55
Keywords: Root system, root polytope, triangulation, Borel subalgebra, abelian ideal, abelian nilradical
@article{ALCO_2018__1_1_115_0,
     author = {Cellini, Paola},
     title = {Triangulations of root polytopes},
     journal = {Algebraic Combinatorics},
     pages = {115--145},
     publisher = {MathOA foundation},
     volume = {1},
     number = {1},
     year = {2018},
     doi = {10.5802/alco.7},
     mrnumber = {3857162},
     zbl = {06882337},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2018__1_1_115_0/}
}
Cellini, Paola. Triangulations of root polytopes. Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 115-145. doi : 10.5802/alco.7. https://alco.centre-mersenne.org/item/ALCO_2018__1_1_115_0/

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