Cambrian frameworks for cluster algebras of affine type
arXiv:1504.00260 · doi:10.1090/tran/7193
Abstract
We give a combinatorial model for the exchange graph and g-vector fan associated to any acyclic exchange matrix B of affine type. More specifically, we construct a reflection framework for B in the sense of [N. Reading and D. E. Speyer, "Combinatorial frameworks for cluster algebras"] and establish good properties of this framework. The framework (and in particular the g-vector fan) is constructed by combining a copy of the Cambrian fan for B with an antipodal copy of the Cambrian fan for -B.
41 pages, 14 figures. Version 2: Expository changes in introduction and in background on cluster algebras. Version 3: Minor changes and corrections. (We acknowledge helpful suggestions by anonymous referees.)