Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin, and A. Zelevinsky associated to each finite type root system a simple convex polytope, called generalized associahedron. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their g-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer. © 2012 Springer Science+Business Media, LLC.

Polyhedral models for generalized associahedra via Coxeter elements

Stella S.
2013

Abstract

Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin, and A. Zelevinsky associated to each finite type root system a simple convex polytope, called generalized associahedron. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their g-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer. © 2012 Springer Science+Business Media, LLC.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/166095
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 19
social impact