Study of general hypergeometric functions and integrable systems coming from monodromy preserving deformation
| Project/Area Number |
23540247
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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 |
Global analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HARAOKA Yoshishige 熊本大学, 自然科学研究科, 教授 (30208665)
NOUMI Masatoshi 神戸大学, 理学系研究科, 教授 (80164672)
IWASAKI Katsunori 北海道大学, 理学研究院, 教授 (00176538)
SAKAI Hidetaka 東京大学, 数理科学研究科, 准教授 (50323465)
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| Research Collaborator |
NAGOYA Hajime
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 特殊関数 / 可積分系 / Twistor theory / Radon transform / 超幾何関数 / 準直交多項式 / モノドロミー保存変形 / 一般Schlesinger系 / Grassmann多様体上の超幾何関数 / 一般シュレジンガー方程式 / Twistor理論 / 一般超幾何関数 / q-超幾何関数 / 量子Grassmann多様体 / 量子群 / 量子パンルベ系 |
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| Outline of Final Research Achievements |
Among special functions, which have good properties, we know the Guass hypergeometric function and Painleve functions which can be characterized by differential equations, integral representations, and contiguity relations. Our study is to generalize and describe them in a unified way. This viewpoint enables to understand why the good properties hold for these objects. The general hypergeometric systems (GHGS) and the general Schlesinger systems (GSS), which generalize Gauss hypergeometric equation and Painleve equations, respectively, are both defined on the Grassmannian manifold. We gave the explicit form of monodromy preserving deformation which gives GSS. We studied, by examining the results of Shah and Woodhouse, when GSS has solutions expressed by the solutions of GHGS and how these solutions can be expressed using solutions of GHGS. As a by-product, we found the relation between the theory of semi-classical orthogonal polynomials and the particular solutions of GSS.
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Report
(6 results)
Research Products
(13 results)
