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1997 Fiscal Year Final Research Report Summary

Studies on the Painleve equations

Research Project

Project/Area Number 08454005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

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)

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)
Project Period (FY) 1996 – 1997
KeywordsPainleve equations / Special polynomials / Baecklund transformations
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.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] H.UMEMURA: "Galoir theory of algebrain and differential equaters" Nagoya Math.J.144. 1-58 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.UMEMURA: "Differential Galuig theory of infinite dimension" Nagoya Math.J.144. 59-135 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.UMEMURA: "Lie-Drach-Vesiof Theory" Adv.Shudies in Pure Math.25. 364-358 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.UMEMURA: "Solutions of the second and fouilh Painleve equations" Nagoya Math.J.148. 151-198 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.UMEMURA: "Special polynomials asociated noth the Painleve equations" Proc.Workshop on the special functions. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.UMEMURA: "Iireducifility of the Painleve equations" Proc.Workshop on the special functions. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Umemura: "Galois theory of algebraic and differential Equations" Nagoya Math.J.144. 1-58 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Umemura: "Differential Galois theory of infinte Dimension" Nagoya Math.J.144. 59-135 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Umemura: "Lie-Drach-Vessiot theory" Adv.Studies in Pure Math.25. 346-358 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Umemura: "Solutions of the second and fourth Painleve equations" Nagoya Math.J.148. 151-198 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Umemura: "Special polynomials associated with the Painleve equations, to appear" Proc.Workshop on Special functions, Montreal. (1996)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Umemura: "Irreducibility of the Painleve equations to appear" Proc.Workshop on Special functions, Montreal. (1996)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-03-16  

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