2004 Fiscal Year Final Research Report Summary
Defining manifolds and symmetries of nonlinear special functions in several variables
| Project/Area Number |
13440054
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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 | Kobe University |
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Principal Investigator |
TAKANO Kyochi Kobe University, Faculty of Science, Professor, 理学部, 教授 (10011678)
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| Co-Investigator(Kenkyū-buntansha) |
NOUMI Masatoshi Kobe University, Graduate School of Science and Technology, Professor, 自然科学研究科, 教授 (80164672)
YAMADA Yasuhiko Kobe University, Faculty of Science, Professor, 理学部, 教授 (00202383)
SAITO Masa-hiko Kobe University, Faculty of Science, Professor, 理学部, 教授 (80183044)
増田 哲 神戸大学, 自然科学研究科, 助手 (00335457)
IWASAKI Katsunori Kyushu University, Faculty of Mathematics, Professor, 数理学研究院, 教授 (00176538)
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| Project Period (FY) |
2001 – 2004
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| Keywords | Garnier system / Degenerate Garnier system / Painleve equation / Defining manifold / Space of initial conditions / Backlund transformation / Confluence / Riemann-Hilbert correspondence |
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| Research Abstract |
1.We have constructed the defining manifolds of the Garnier system and all its degenerate systems in two varibales. We have also solved the same problem for the Noumi-Yamada system of type A^<(1)>_4.
2.We have proved that the manifold defined by means of Backlund transformation group for each Painleve equation is isomorphic to the corresponding defining manifold constructed by K.Okamoto.
3.We have shown that there exists an hierarchy in the Backlund transformation groups for Painleve equations, namely, the Backlund transformation groups for all Painleve equations can be obtained successively from that for the sixth Painleve equation by the use of the usual confluence procedures.
4.We have characterized the Backlund transformation group for the sixth Painleve equation by means of Riemann-Hilbert correspondence, namely, the correspondence from the phase space(the space of initial conditions) of the sixth Painleve equation to the moduli space of the monodromy representation is just a covering mapping with the affine Weyl group of type D^<(1)>_4 as the covering transformation group.
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