| Autor: |
Chris Fraser |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 28th... (2020) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.6395 |
| Popis: |
We provide bijections between the cluster variables (and clusters) in two families of cluster algebras which have received considerable attention. These cluster algebras are the ones associated with certain Grassmannians of k-planes, and those associated with certain spaces of decorated SLk-local systems in the disk in the work of Fock and Goncharov. When k is 3, this bijection can be described explicitly using the combinatorics of Kuperberg's basis of non-elliptic webs. Using our bijection and symmetries of these cluster algebras, we provide evidence for conjectures of Fomin and Pylyavskyy concerning cluster variables in Grassmannians of 3-planes. We also prove their conjecture that there are infinitely many indecomposable nonarborizable webs in the Grassmannian of 3-planes in 9-dimensional space. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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