Cluster Configuration Spaces of Finite Type
For each Dynkin diagram , we define a ''cluster configuration space'' ℳ and a partial compactification ℳ˜. For = ₙ₋₃, we have ℳₙ₋₃ = ℳ₀,ₙ, the configuration space of points on ℙ¹, and the partial compactification ℳ˜ₙ₋₃ was studied in this case by Brown. The space M˜ is a smooth...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211435 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Cluster Configuration Spaces of Finite Type. Nima Arkani-Hamed, Song He and Thomas Lam. SIGMA 17 (2021), 092, 41 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | For each Dynkin diagram , we define a ''cluster configuration space'' ℳ and a partial compactification ℳ˜. For = ₙ₋₃, we have ℳₙ₋₃ = ℳ₀,ₙ, the configuration space of points on ℙ¹, and the partial compactification ℳ˜ₙ₋₃ was studied in this case by Brown. The space M˜ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ℳ˜ are generated by coordinates uγ, in bijection with the cluster variables of type , and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.
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| ISSN: | 1815-0659 |