2017 Fiscal Year Final Research Report
Melting crystal models and quantum torus symmetry
| Project/Area Number |
15K04912
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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 | Setsunan University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
高崎 金久 近畿大学, 理工学部, 教授 (40171433)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | ランダム歪平面分割 / 位相的頂点の理論 / 量子トーラス代数 / 位相的開弦振幅 / 量子リーマン曲線 / q-差分方程式 / 可積分階層 |
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| Outline of Final Research Achievements |
Random plane partition or melting crystal model was a topic in the branch of combinatorics. However, it has been found surprising relations with other branches in modern mathematical physics, such as the Seiberg-Witten theory of supersymmetric gauge theories, the Gromov-Witten theory and the mirror symmetry of Calabi-Yau 3-folds. The model has been also studied from the integrable system viewpoint. We further elucidate integrable structure of melting crystal models, using quantum torus symmetry. All genus open string amplitudes on closed topological vertex are computed in a closed form, and thereby the underlying quantum curve is obtained. It turns out to be expressed as the q-difference operator which is a q-analogue of the Kac-Schwarz operator of random matrix or 2-dimensional quantum gravity. By giving a generalization of the shift symmetry of quantum torus, the relation between three-partition Hodge integral and random skew plane partition is derived.
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| Free Research Field |
無限次元可積分系
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