Studies on the partition functions of quantum integrable models and representation theory of symmetric polynomials
| Project/Area Number |
15H06218
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
Kohei Motegi 東京海洋大学, 学術研究院, 助教 (30583033)
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 量子可積分系 / 可解格子模型 / 対称多項式 / 表現論 / 組合せ論 / 分配関数 / 組み合わせ論 |
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| Outline of Final Research Achievements |
We studied two types of integrable six-vertex models: the Felderhof free-fermionic model and the XXZ-type six-vertex model. As for the Felderhof free-fermionic model, we investigated the dual wavefunctions, and derived the exact correspondence with the symmetric functions. As a consequence of the result, we derived a new combinatorial formula for the Schur functions. We extended the correspondence to the reflecting boundary conditions and proved that the dual wavefunctions are expressed as the symplectic Schur functions.
As for the XXZ-type six-vertex model, we made the Izergin-Korepin analysis on the domain wall boundary partition functions, and proved that certain symmetric funtions satsify the require properties. Moreover, we have succeeded in extending the analysis to the waveufunctions which is a more general class of partition functions. To accomplish this, we extended the Izergin-Korepin analysis from the classical domain wall boundary partition functions to the wavefunctions.
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Report
(3 results)
Research Products
(3 results)
