Categorification of special function
| Project/Area Number |
17K18726
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra, Geometry, and related fields
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| Research Institution | Kyushu University |
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Principal Investigator |
OCHIAI HIROYUKI 九州大学, マス・フォア・インダストリ研究所, 教授 (90214163)
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| Research Collaborator |
Dorjgotov Khongorzul モンゴル国立大学
Zunderiya Uuganbayar モンゴル国立大学
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| Project Period (FY) |
2017-06-30 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2018: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Keywords | 特殊関数 / リー環 / 変数分離 / 超幾何関数 / 一般ライト関数 / 対称性 / 分数階微分 / 圏論 / D加群 / 母関数 / 軌道分解 |
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| Outline of Final Research Achievements |
Separation of variables is one of the origin of special functions. We determine the symmetry of a fractional partial differential equation, and discuss the scheme of the separation of variables in fractional case. As well as the decomposition of the manifold by the group action, the choice of independent variables are shown to be a key of the separation of variables, especially in the fractional case. As a corollary, we obtain a new expression of solution of such a fractional partial differential equation in terms Mittag-Leffler functions and generalized Wright functions. We also give the system of the fundamental equations on the coefficient functions, and with the help of inductive structure, we are able to determine the symmetry Lie algebra for a fractional partial differential equations.
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| Academic Significance and Societal Importance of the Research Achievements |
特殊関数の一つの典型的な現れ方として、群作用に関する軌道分解によって偏微分方程式系から常微分方程式を得るプロセスがあるが、これを圏化するスキームを考えた。特に軌道分解が直既約とならない場合に軌道分解の複雑さを記述する関数系として特殊関数は、古典的に複比の持つ不変式的な構造と、ブリューア分解の持つ離散組み合わせ的な構造を併せ持つものであり、圏化によるアプローチに優位性があるものである。
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Report
(3 results)
Research Products
(16 results)
