ALGEBRAIC COMBINATORICS

no. 1
Triangulations of root polytopes
Cellini, Paola1
1 Università di Chieti e Pescara Dipartimento di Ingegneria e Geologia Viale Pindaro 42 65127 Pescara PE Italy
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.

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Published online:
DOI: 10.5802/alco.7
Classification: 17B20, 17B22, 20F55
Keywords: Root system, root polytope, triangulation, Borel subalgebra, abelian ideal, abelian nilradical
Cellini, Paola 1

1 Università di Chieti e Pescara Dipartimento di Ingegneria e Geologia Viale Pindaro 42 65127 Pescara PE Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.7/

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