• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study of general hypergeometric functions and integrable systems coming from monodromy preserving deformation

Research Project

Project/Area Number 23540247
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionKumamoto University

Principal Investigator

KIMURA Hironobu  熊本大学, 自然科学研究科, 教授 (40161575)

Co-Investigator(Renkei-kenkyūsha) HARAOKA Yoshishige  熊本大学, 自然科学研究科, 教授 (30208665)
NOUMI Masatoshi  神戸大学, 理学系研究科, 教授 (80164672)
IWASAKI Katsunori  北海道大学, 理学研究院, 教授 (00176538)
SAKAI Hidetaka  東京大学, 数理科学研究科, 准教授 (50323465)
Research Collaborator NAGOYA Hajime  
Project Period (FY) 2011-04-28 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords特殊関数 / 可積分系 / Twistor theory / Radon transform / 超幾何関数 / 準直交多項式 / モノドロミー保存変形 / 一般Schlesinger系 / Grassmann多様体上の超幾何関数 / 一般シュレジンガー方程式 / Twistor理論 / 一般超幾何関数 / q-超幾何関数 / 量子Grassmann多様体 / 量子群 / 量子パンルベ系
Outline of Final Research Achievements

Among special functions, which have good properties, we know the Guass hypergeometric function and Painleve functions which can be characterized by differential equations, integral representations, and contiguity relations. Our study is to generalize and describe them in a unified way. This viewpoint enables to understand why the good properties hold for these objects. The general hypergeometric systems (GHGS) and the general Schlesinger systems (GSS), which generalize Gauss hypergeometric equation and Painleve equations, respectively, are both defined on the Grassmannian manifold. We gave the explicit form of monodromy preserving deformation which gives GSS. We studied, by examining the results of Shah and Woodhouse, when GSS has solutions expressed by the solutions of GHGS and how these solutions can be expressed using solutions of GHGS. As a by-product, we found the relation between the theory of semi-classical orthogonal polynomials and the particular solutions of GSS.

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (13 results)

All 2016 2015 2014 2013 2012 2011 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (6 results) (of which Int'l Joint Research: 3 results,  Invited: 6 results)

  • [Journal Article] General Schlesinger Systems and Their Symmetry from the View Point of Twistor theory2013

    • Author(s)
      Hironobu Kimura, Damiran Tseveenamijil
    • Journal Title

      Journal of Nonlinear Mathematical Physics

      Volume: 20, Supplement 1 Issue: Supplement 1 Pages: 130-152

    • DOI

      10.1080/14029251.2013.862441

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Regular coordinates and deformation equations for Fuchsian systems2012

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Banach Center Publications

      Volume: 97 Pages: 39-58

    • DOI

      10.4064/bc97-0-3

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On a problem of arragements related to the hypergeometric integrals of confluent type2012

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 62 Pages: 137-155

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangement2012

    • Author(s)
      Yoshishige Haraoka
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 62 Pages: 109-136

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Wronskian determinant formulas of the general hypergeometric functions2011

    • Author(s)
      Hironobu Kimura
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 34 Pages: 507-524

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] A connection problem for Simpson's even family of rank four2011

    • Author(s)
      Yoshishige Haraoka (and Katsuhisa Mimachi)
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 54 Pages: 495-515

    • NAID

      130001271656

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 大域解析可能なFuchs型方程式2011

    • Author(s)
      原岡喜重
    • Journal Title

      数学

      Volume: 63 Pages: 257-280

    • NAID

      10029849848

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Relation of semi-classical orthogonal polynomials to the general Schlesinger systems2016

    • Author(s)
      Hironobu Kimura
    • Organizer
      International Conference on Partial Differential Equations: General Theory and Variational Problems
    • Place of Presentation
      Philippines, Cebu
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Orthogonal polynomials and General Schlesinger systems2015

    • Author(s)
      Hironobu Kimura
    • Organizer
      Analytic, Algebraic and Geometric Aspects of Differential Equations
    • Place of Presentation
      Polandm, Bedlewo
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] General Schlesinger systems and Ward Ansatz solutions2015

    • Author(s)
      Hironobu Kimura
    • Organizer
      Recent progress of integrable systems
    • Place of Presentation
      Taipei, Institute of Mathematics in Academia Sinica
    • Year and Date
      2015-04-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Orthogonal polynomials and General Schlesinger systems2014

    • Author(s)
      木村弘信
    • Organizer
      研究集会「微分方程式の展望」
    • Place of Presentation
      Kumamoto University
    • Year and Date
      2014-10-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On q-integral for q-hypergeometric functions2013

    • Author(s)
      木村弘信
    • Organizer
      Recent Progress in the Painleve equations: algebraic, asymptotic and topological
    • Place of Presentation
      France,Universite de Strasbourg
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Introduction to the hypergeometric functions on the Grassmannian manifold

    • Author(s)
      Hironobu Kimura
    • Organizer
      Representation theory seminar
    • Place of Presentation
      Mathematical Institute of National University of Mongolia, Ulaanbaatar, Mongolia
    • Related Report
      2012 Research-status Report
    • Invited

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi