Geodesic
Root polytopes and abelian ideals
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 607-645.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study the root polytope $\mathcal{P}_\varPhi$ of a finite irreducible crystallographic root system $\varPhi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\varPhi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal{P}_\varPhi$ and analyze its relation with the facets of $\mathcal{P}_\varPhi$. For $\varPhi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal{P}_\varPhi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal{P}_\varPhi^+$.
Classification : 05E10, 05E15, 52C07
Keywords: root system, root polytope, Weyl group, Borel subalgebra, abelian ideal 
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     author = {Cellini, Paola and Marietti, Mario},
     title = {Root polytopes and abelian ideals},
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     language = {en},
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Cellini, Paola; Marietti, Mario. Root polytopes and abelian ideals. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 607-645. http://geodesic.mathdoc.fr/item/JAC_2014__39_3_a7/