Let P_\Phi be the root polytope of a finite irreducible crystallographic root system \Phi, i.e., the convex hull of all roots in \Phi. The polar of P_\Phi, denoted P*_\Phi, coincides with the union of the orbit of the fundamental alcove under the action of the Weyl group. In this paper, we determine which polytopes P*_\Phi are zonotopes and which are not. The proof is constructive.
Polar root polytopes that are zonotopes / Cellini, Paola; Marietti, Mario. - In: SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE. - ISSN 1286-4889. - 73:(2015).
Polar root polytopes that are zonotopes
MARIETTI, Mario
2015-01-01
Abstract
Let P_\Phi be the root polytope of a finite irreducible crystallographic root system \Phi, i.e., the convex hull of all roots in \Phi. The polar of P_\Phi, denoted P*_\Phi, coincides with the union of the orbit of the fundamental alcove under the action of the Weyl group. In this paper, we determine which polytopes P*_\Phi are zonotopes and which are not. The proof is constructive.File in questo prodotto:
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