Polytopal realizations of finite type $\mathbf{g}$-vector fans

Abstract

This paper shows the polytopality of any finite type $\mathbf{g}$-vector fan, acyclic or not. In fact, for any finite Dynkin type $\Gamma$, we construct a universal associahedron ${\mathsf{Asso}}_{\mathrm{un}}(\Gamma )$ with the property that any $\mathbf{g}$-vector fan of type $\Gamma$ is the normal fan of a suitable projection of ${\mathsf{Asso}}_{\mathrm{un}}(\Gamma )$.

27 pages, 9 figures; Version 2: Minor changes in the introduction

References in corpus (2)

• Mutations of group species with potentials and their representations. Applications to cluster algebras
• Geometric realizations of the accordion complex of a dissection

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