基于Coxeter元的广义协面体多面体模型
Polyhedral models for generalized associahedra via Coxeter elements
摘要：
受簇代数理论的启发，F. Chapoton，S. Fomin和A. Zelevinsky关联到每个有限型根系一个简单的凸多胞体称为\emph{generalized associahedron}。他们提供了一个明确的实现这个多面体与一个二分方向的相应Dynkin图。在本文的第一部分中，使用由S.- W. Yang和A. Zelevinsky，我们将原始结构推广到任何方向。第二部分证明了我们的构造与C.霍尔韦格角Lange和H. Thomas在由N. Reading和D.斯派尔
英文摘要：
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 \emph{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.
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