Séminaire Lotharingien de Combinatoire, B61Aa (2009), 13 pp.

Nantel Bergeron, Christophe Hohlweg, Carsten Lange and Hugh Thomas

Isometry Classes of Generalized Associahedra

Abstract. Let W be a finite Coxeter group. Generalized associahedra are convex polytopes constructed from a permutahedron of W and an orientation of the Coxeter graph of W. They play a fundamental role in the theory of finite type cluster algebras initiated by Fomin and Zelevinsky, and also appear in algebraic topology. In this article, we show that the isometries of these polytopes are given by certain automorphisms of oriented Coxeter graphs.

Received: May 15, 2008. Accepted: October 16, 2008. Final Version: October 16, 2008.

The following versions are available: