English

Cluster scattering diagrams of acyclic affine type

Combinatorics 2025-08-04 v4 Representation Theory

Abstract

We give an explicit construction of the cluster scattering diagram for any acyclic exchange matrix of affine type. We show that the corresponding cluster scattering fan coincides both with the mutation fan and with a fan constructed in the almost-positive roots model.

Keywords

Cite

@article{arxiv.2205.05125,
  title  = {Cluster scattering diagrams of acyclic affine type},
  author = {Nathan Reading and Salvatore Stella},
  journal= {arXiv preprint arXiv:2205.05125},
  year   = {2025}
}

Comments

45 pages, 2 figures. Version 2: Fixed typographical error. Version 3: Fixed an error in the proof of a main result, corrected typos, other minor changes. Version 4: Corrected typos, other minor changes. We thank an anonymous referee for many helpful comments