Timeline for Scattering diagram for the cluster algebra $ \mathbb C [N]$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2019 at 20:53 | history | edited | Joel Kamnitzer | CC BY-SA 4.0 |
added 457 characters in body
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| Jun 30, 2019 at 20:47 | comment | added | Joel Kamnitzer | Thanks for your comments. I am editing my question to ask it more precisely. | |
| Jun 25, 2019 at 10:41 | comment | added | Jan Grabowski | Also, in my view, I don't think we really know very much explicit about the $\mathbb{C}[N]$ cluster algebras beyond suitable initial data, as Geiss-Leclerc-Schroer's approach is more sophisticated and geometric. I don't think I could easily "read off" information you'd want for a scattering diagram. (But perhaps others who know better can.) | |
| Jun 25, 2019 at 10:40 | comment | added | Jan Grabowski | Since I can't be sure the answer to the question as asked is no, I'm putting this in a comment instead: I don't believe so. For $n>5$ (or possibly $6$; I'm always out by one), the cluster structure is "wild" - infinite type, and very complicated, just like the canonical basis is. For very small $n$, the answer will be yes (see e.g. a talk of Mark Gross, dpmms.cam.ac.uk/~mg475/clusters.pdf) because they're finite type and easy. | |
| Jun 24, 2019 at 6:53 | comment | added | Joel Kamnitzer | I should add that Magee's article (which David linked to) is quite nice, as his followup one (front.math.ucdavis.edu/1709.05776) which treats invariants in triple tensor products. These papers show that the GHKK theory applies to the representation theoretic situations. However, they don't give any description of the resulting bases or the scattering diagrams. | |
| Jun 23, 2019 at 19:56 | comment | added | Joel Kamnitzer | I've read that article, which partially piqued my interest in the subject. However, it doesn't compute the scattering diagram. (Also, there is an error in the description of the theta basis in that paper.) | |
| Jun 23, 2019 at 18:00 | comment | added | David E Speyer | Does arxiv.org/abs/1502.03769 help? | |
| Jun 23, 2019 at 16:44 | history | asked | Joel Kamnitzer | CC BY-SA 4.0 |