Geodesic
Permutonestohedra
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 1, pp. 125-155.

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

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the corresponding real De Concini-Procesi models. In this paper, starting from any root system $\Phi$ with finite Coxeter group $W$ and any $W$-invariant building set, we describe an explicit realization of the real spherical model as a union of polytopes (nestohedra) that lie inside the chambers of the arrangement. The main point of this realization is that the convex hull of these nestohedra is a larger polytope, a permutonestohedron, equipped with an action of $W$ or also, depending on the building set, of $\mathrm{Aut}(\Phi)$. The permutonestohedra are natural generalizations of Kapranov's permutoassociahedra.
Classification : 52B05, 20F55
Keywords: models of arrangements, Coxeter groups, nestohedra 
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     author = {Gaiffi, Giovanni},
     title = {Permutonestohedra},
     journal = {Journal of Algebraic Combinatorics},
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     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__41_1_a3/}
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Gaiffi, Giovanni. Permutonestohedra. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 1, pp. 125-155. http://geodesic.mathdoc.fr/item/JAC_2015__41_1_a3/