Permutahedra and generalized associahedra

Hohlweg, Christophe; Lange, Carsten E.M.C. et Thomas, Hugh (2011). « Permutahedra and generalized associahedra ». Advances in Mathematics, 226(1), pp. 608-640.

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Résumé

Given a finite Coxeter system (W,S)(W,S) and a Coxeter element c, or equivalently an orientation of the Coxeter graph of W , we construct a simple polytope whose outer normal fan is N. Reading's Cambrian fan Fc, settling a conjecture of Reading that this is possible. We call this polytope the c-generalized associahedron. Our approach generalizes Loday's realization of the associahedron (a type A c-generalized associahedron whose outer normal fan is not the cluster fan but a coarsening of the Coxeter fan arising from the Tamari lattice) to any finite Coxeter group. A crucial role in the construction is played by the c-singleton cones, the cones in the c-Cambrian fan which consist of a single maximal cone from the Coxeter fan. Moreover, if W is a Weyl group and the vertices of the permutahedron are chosen in a lattice associated to W, then we show that our realizations have integer coordinates in this lattice.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Coxeter groups; Cambrian fans; Cambrian lattices; Generalized associahedron; Cluster fans
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Christophe Hohlweg
Date de dépôt:	15 févr. 2016 15:04
Dernière modification:	20 avr. 2016 19:31
Adresse URL :	http://archipel.uqam.ca/id/eprint/7808

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