2010 Fiscal Year Final Research Report
Representations of quantum groups and quantum integrable systems
| Project/Area Number |
19540021
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
NAKANISHI Tomoki Nagoya University, 多元数理科学研究科, 准教授 (80227842)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 量子群 / 量子可積分系 / 団代数 / 団圏 / Y-system / T-system / dilogarithm |
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| Research Abstract |
We clarify the relation between cluster algebras and the T- and Y-systems, which are functional equations originated from Bethe ansatz method. Using the cluster algebraic formulation, we prove the periodicities of Y-systems and the associated dilogarithm identities, which have remained as conjectures for twenty years. We also clarify various theorems and properties of cluster algebras.
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