2017 Fiscal Year Final Research Report
Integrable structures in mathematical physics and combinatorics
| Project/Area Number |
25400111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kindai University (2014-2017)
Kyoto University (2013) |
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Principal Investigator |
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| Research Collaborator |
NAKATSU Toshio
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | melting crystal model / gauge theory / topological string / Young diagram / quantum torus algebra / quantum dilogarithm / quantum curve / integrable hierarchy |
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| Outline of Final Research Achievements |
The melting crystal model, 4D and 5D supersymmetric gauge theory and topological string theory on local toric Calabi-Yau manifolds have a common feature that the partition functions can be formulated in the language of Young diagrams.
We found that the KP hierarchy, the Toda hierarhy and their reductions underlie these models of mathematical physics and their variants. In the course of this research, new computational techniques based on the quantum torus algebra and the quantum diloarithmic functions were also developed. Moreover, we derived the quantum mirror (or spectral) curves associated with these models from the integrable structures, and pointed out that they are analogues of the Kac-Schwarz operators that have been known in the theory of integrable hierarchies.
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| Free Research Field |
代数解析学，数理物理学，可積分系
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