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

Abstract

This paper shows the polytopality of any finite type g\mathbf{g}-vector fan, acyclic or not. In fact, for any finite Dynkin type Ξ“\Gamma, we construct a universal associahedron Assoun(Ξ“)\mathsf{Asso}_{\mathrm{un}}(\Gamma) with the property that any g\mathbf{g}-vector fan of type Ξ“\Gamma is the normal fan of a suitable projection of Assoun(Ξ“)\mathsf{Asso}_{\mathrm{un}}(\Gamma).Comment: 27 pages, 9 figures; Version 2: Minor changes in the introductio

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