Discretization of higher order Painleve system and rigid system
| Project/Area Number |
15K04911
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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 |
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Principal Investigator |
SUZUKI Takao 近畿大学, 理工学部, 准教授 (60527208)
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| Research Collaborator |
Okubo Naoto 青山学院大学
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | パンルヴェ方程式 / 離散可積分系 / リー代数 / クラスター代数 / ワイル群 / 超幾何函数 / 超幾何関数 |
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| Outline of Final Research Achievements |
Recently higher order generalizations of the Painleve equations are proposed both on continuous side and on discrete side. However we haven't clarified yet a classification of equations or a relationship with hypergeometric functions. In this work we have formulated birational representations of a reducible extended affine Weyl group with the aid of cluster mutations. Translations of this group provide the known higher order q-Painleve equations containing the q-hypergeometric functions as particular solutions.
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| Academic Significance and Societal Importance of the Research Achievements |
高階パンルヴェ方程式の分類問題は，2階の場合と比べて初期値空間の代数幾何が難しくなることもあって，未だ有効な手段が発見されていない．微分の場合にはKatz，原岡，大島らによって確立された分類理論が存在するが，差分の場合については未だ想像もつかない．本研究の結果は，この問題を解決するための一つのきっかけとなるかもしれない．また，クラスター代数との関連が明らかにされたことで，正準量子化や共形場理論の方面への更なる発展も期待出来る．
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Report
(5 results)
Research Products
(19 results)
