1997 Fiscal Year Final Research Report Summary
Studies on the Painleve equations
| Project/Area Number |
08454005
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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 |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
UMEMURA Hiroshi Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (40022678)
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| Co-Investigator(Kenkyū-buntansha) |
MUKAI Shigeru Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (80115641)
NAMIKAWA Yukihiko Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (20022676)
KITOKA Yosiyuki Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (40022686)
TSUCHIYA Akohiro Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (90022673)
AOMOTO Kazuhiko Nagoya University, Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (00011495)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Painleve equations / Special polynomials / Baecklund transformations |
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| Research Abstract |
(1) We succeeded in generating special polynomials by Painleve equations, which generalize the Yablonskii-Vorob'ev polynomial for the second Painleve equation and the Okamoto polynomial for the fourth Painleve equation, Polynomials of particular interest appeared in algebraic solutions of the third, the fifth, and the sixth equations.
(2) As for the polynomials associated with algebraic solutions of the sixth equation, we formulated a conjecture that each coefficient of the polynomials is equal to the degree of the representation of GL given by an explicit Young diagram.
(3) The above conjecture was recently settled.
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