Cluster Structures and Subfans in Scattering Diagrams
We give more precise statements of the Fock-Goncharov duality conjecture for cluster varieties parametrizing SL₂/PGL₂-local systems on the once-punctured torus. Then we prove these statements. Along the way, using distinct subfans in the scattering diagram, we produce an example of a cluster variety...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210597 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Cluster Structures and Subfans in Scattering Diagrams. Yan Zhou. SIGMA 16 (2020), 013, 35 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We give more precise statements of the Fock-Goncharov duality conjecture for cluster varieties parametrizing SL₂/PGL₂-local systems on the once-punctured torus. Then we prove these statements. Along the way, using distinct subfans in the scattering diagram, we produce an example of a cluster variety with two non-equivalent cluster structures. To overcome the technical difficulty of infinite non-cluster wall-crossing in the scattering diagram, we introduce quiver folding into the machinery of scattering diagrams and give a quotient construction of scattering diagrams.
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| ISSN: | 1815-0659 |