2010 Fiscal Year Final Research Report
Study on hypergeometric functions
| Project/Area Number |
19340034
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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 |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
YOSHIDA Masaaki Kyushu University, 大学院・数理学研究院, 教授 (30030787)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 黒写像 / 又黒写像 / 平前曲面 / 超幾何関数 / 絵有関数 / 離散曲面 / 平面配置 |
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| Research Abstract |
We succeeded to find a good discretization of the hyperbolic Schwarz map for the Airy equation. This is the starting point of the study of singularities of discrete surfaces. For the hypergeometric differential equation of type (3,6), we found a relation between the two monodromy groups - arithmetic group acting of the domain of type IV, and the maximal non-real finite complex reflection group.
We described chambers cut out by six planes in general position in the 3-space.
Veronese arrangements of hyperplanes in real projective spaces re studied.
A set of generators of the monodromy group of the Appell-Lauricella's hypergeometric equation of type FA is obtained.
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