Five years ago, Gross-Hacking-Keel-Konstsevich made a major advance in the theory of cluster algebras, by constructing bases of cluster algebras in large generality. A key tool in their construction is the theory of scattering diagrams.

Some examples of scattering diagrams are described in the literature, especially for rank 2 cluster algebras. However, for me they remain somewhat mysterious.

I am interested in cluster algebras arising from semisimple groups, especially the algebra $ \mathbb C[N] $ of functions on the maximal unipotent subgroup of a semisimple group? (For example, for $ SL_n$, this is the group of uni-upper triangular matrices.)

Question Has anyone has described/computed the scattering diagram associated to the cluster algebra $ \mathbb C[N] $?

If this example is too complicated, I would also be happy with understanding the scattering diagrams associated to the subalgebras $ \mathbb C[N(w)] $ or the coordinate rings of partial flag varieties.

Five years ago, Gross-Hacking-Keel-Kontsevich made a major advance in the theory of cluster algebras, by constructing bases of cluster algebras in large generality. A key tool in their construction is the theory of scattering diagrams.

Some examples of scattering diagrams are described in the literature, especially for rank 2 cluster algebras. However, for me they remain somewhat mysterious.

I am interested in cluster algebras arising from semisimple groups, especially the algebra $ \mathbb C[N] $ of functions on the maximal unipotent subgroup of a semisimple group? (For example, for $ SL_n$, this is the group of uni-upper triangular matrices.)

Question:

Has anyone has described/computed the scattering diagram associated to the cluster algebra $ \mathbb C[N] $?

If this example is too complicated, I would also be happy with understanding the scattering diagrams associated to the subalgebras $ \mathbb C[N(w)] $ or the coordinate rings of partial flag varieties.

Updated question:

Since $ \mathbb C[N] $ is not a finite-type cluster algebra (unless $ G = SL_2, \dots, SL_5$) it seems to be impossible to completely describe the scattering diagram. However, perhaps it is possible to give a rough description of it, for example in Figure 1.3 of GHKK, they describe the appearance of the rank 2 scattering diagrams of non-finite type. Is it possible to give an analogous description for $ \mathbb C[N] $?