2010 Fiscal Year Final Research Report
Toward a unified understanding of general hypergeometric functions and general Schlesinger system by twistor theory
| Project/Area Number |
19340041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
KIMURA Hironobu Kumamoto University, 大学院・自然科学研究科, 教授 (40161575)
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| Co-Investigator(Kenkyū-buntansha) |
HARAOKA Yoshishige 熊本大学, 大学院・自然科学研究科, 教授 (30208665)
TANABE Susumu 熊本大学, 大学院・自然科学研究科, 教授 (90432997)
MISAWA Masashi 熊本大学, 大学院・自然科学研究科, 教授 (40242672)
FURUSHIMA Mikio 熊本大学, 大学院・自然科学研究科, 教授 (00165482)
OKAMOTO Kazuo 大学評価・学位授与機構, 国際連携センター, 理事 (40011720)
IWASAKI Katsunori 北海道大学, 大学院・理学研究科, 教授 (00176538)
SHIMOMURA Shun 慶応大学, 理工学部, 教授 (00154328)
KAWAMUKO Hiroyuki 三重大学, 教育学部, 准教授 (00303719)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数方程式の大域理論 / Yang-Mills / Schlesinger系 / 可積分系 / 超幾何関数 / Twistor理論 |
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| Research Abstract |
We studied the theory of general hypergeometric functions(HGF) which generalize important special functions, like as Gauss hypergeometric functions, governed by linear differential equations to functions of several variables. We also studied nonlinear differential equations called general Schlesinger systems(GSS), which describe families of linear systems preserving monodromy data, from the point of view of twistor theory. For HGF, we determined the cohomology groups which are defined using the integrand of the integral representation of HGF. For GSS, we constructed its solutions expressed using HGF.
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