2004 Fiscal Year Final Research Report Summary
Stratification, exterior power structure, asymptotic behavior and connection coefficients for confluenthypergeometric functions
| Project/Area Number |
13440057
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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 |
HARAOKA Yoshishige Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (30208665)
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| Co-Investigator(Kenkyū-buntansha) |
KIMURA Hironobu Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (40161517)
KOHNO Mitsuhiko Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (30027370)
FURUSHIMA Mikio Kumamoto University, Faculty of Science, Professor, 理学部, 教授 (00165482)
INOUE Hisao Kumamoto University, Faculty of Science, Lecturer, 理学部, 講師 (40145272)
OKA Yukimasa Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (50089140)
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| Project Period (FY) |
2001 – 2004
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| Keywords | hypergeometric function / rigid local system / arrangement of hyperplanes / deformation of differential equations / accessory parameter / confluence |
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| Research Abstract |
In this research we planed to study confluent hypergeometric functions as deformations of weighted arrangements of hypersurfaces. In particular, we planed to analyse the behavior of confluent hypeigeometric functions via geometrical structures of the moduli space. We obtained the following results.
1.Construction of cycles by confluence : We had already constructed 1-dimensional cycles. We generalized the theorem on convergence of the limit in the process of confluence. Also we tried to construct higher-dimensional cycles by confluence, and noticed that they should be constructed in the flag variety.
2.Section of rigid local systems : We proved the existence of integral representations of sections of rigid local systems in a constructive way. The result is different from one by Katz et al. We also analysed Katz integral representations, and noticed that they are special cases of Selberg type integrals. We studied on the basis of the (co) homology.
3.Evaluation of Stokes multipliers : By using integral representations of sections of rigid local systems, we evaluated the Stokes multipliers for the system obtaind by Laplace transform.
4.Rigidity of local systems on higher dimensional spaces : We came to examples of local systems on higher dimensional spaces whose indexes of rigidity vary by coordinate changes. This implies that we need some intrinsic definition of the ridigity for the higher dimensional case.
5.Application to the deformation theory of differential equations : The operations used in constructing rigid local systems can be applied to the study of deformations of differential equations. Some results are obtained.
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[Book] 超幾何関数2002
Author(s)
原岡喜重
Total Pages
197
Publisher
朝倉書店
Description
「研究成果報告書概要(和文)」より
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