Algebraic analysis of difference equations arising from integrable systems
| Project/Area Number |
26400106
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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 | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NAGOYA Hajime 金沢大学, 数物科学系, 准教授 (80447367)
TANAKA Tatsushi 京都産業大学, 理学部, 准教授 (60515196)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 可積分系 / 確率過程 / 多重ゼータ値 / q類似 / q 類似 / 可積分確率過程 / アフィンヘッケ代数 / 量子アフィン代数 / 表現論 |
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| Outline of Final Research Achievements |
We studied algebraic structure of integrable stochastic systems and a q-analogue of multiple zeta values (qMZV). First, we constructed new integrable stochastic systems using a representation of a deformation of the affine Hecke algebra. Regarding the multi-spices q-Boson model, which is an integrable stochastic system constructed as above, we obtained an explicit formula for eigenfunctions of its generator. Second, we found that the finite sum obtained by setting the parameter q in qMZVs to a root of unity simultaneously produces important objects in number theory called finite/symmetrized multiple zeta values.
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Report
(5 results)
Research Products
(13 results)
