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

Studies of D Module and Integrable System

Research Project

Project/Area Number 02452009
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKyoto University

Principal Investigator

SATO Mikio  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (80012201)

Co-Investigator(Kenkyū-buntansha) ARAKI Huzihiro  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027361)
SAITO Kyoji  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20012445)
MIWA Tetsuji  Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (10027386)
KASHIWARA Masaki  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (60027381)
KAWAI Takahiro  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
斎藤 盛彦  京都大学数理解析研究所, 助手 (10186968)
高崎 金久  京都大学数理解析研究所, 助手 (40171433)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1991: ¥2,300,000 (Direct Cost: ¥2,300,000)
KeywordsMicro-Local Analysis / WKB Method / Borel Transform / Crystal Base / Eichler Integral / XY Model / Constant Angle Curve / D Module / 非調和振動子 / ボロス係数 / 量子群 / R行列 / ブレ-ド群 / 格子型模型 / 混合ホッジ加群
Research Abstract

Mikio Sato and Takahiro Kawai studied the singular perturbation theory of the ordinary differential equations by exploiting the method of micro-local analysis. They gave a conjecture about the relation between the WKB method and the Borel transform for unharmonic oscillator equation and its secular equation.
Masaki Kashiwara and Tetsuji Miwa applied the theory of crystal base to the computation of I point functions for a large class called the perfect representations, and obtained the general result that the 1 point function is given by characters.
Kyoji Saito generalized the Eichler integral and constructed doubly infinite series of vector bundles over the moduli spaces of curves.
Huzihiro Araki showed that the return to the equilibrium happens in the perturbed XY model.
Shigetake Matsuitra applied functional analysis to constant angle curve, even in non convex case.
Morihiko Saito applied the theory of Hodge module and D module, and proved Dimca's conjecture about fiber cohomology of polynomial mappings.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 河合 隆裕: "Secular Equations through the Exact WKB Analysis" Preprint RIMSー852. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 柏原 正樹: "Crystallizing the qーAnalogue of Universal Enveloping Algebras" Proc.Int.Congr.Math.791-797 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 柏原 正樹: "On Crystal Bases of the qーAnalogue of Universal Enveloping Algebras" Duke Mathematical Journal. 63. 465-516 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 柏原 正樹: "Global Crystal Bases of Quantum Groups" Preprint RIMSー756. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 斎藤 恭司: "A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces" Publ.RIMS,Kyoto Univ.27. 431-460 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 斎藤 恭司: "The Limit Element in the Configuration Algebra for a Discrete Group:A precis" Proc.Int.Congr.Math.931-942 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KAWAI, Takahiro: "Secular Equations through the Exact WKB Analysis" Preprint. RIMS-852. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KASHIWARA, Masaki: "Crystallizing the q-Analogue of Universal Enveloping Algebras" Proc. Int. Congr. Math.791-797 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KASHIWARA, Masaki: "On Crystal Bases of the q-Analogue of Universal Enveloping Algebras" Duke Mathematical Journal. 63. 465-516 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KASHIWARA, Masaki: "Global Crystal Bases of Quantum Groups" Preprint. RIMS-756. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SAITO, Kyoji: "A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces" Publ. RIMS, Kyoto Univ.27. 431-460 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SAITO, Kyoji: "The Limit Element in the Configuration Algebra for a Discrete Group : A precis" Proc. Int. Congr. Math.931-942 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SAITO, Kyoji: "On a Linear Structure of a Quotient Variety by a Finite Reflexion Group" Preprint. RIMS-753. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] ARAKI, Huzihiro: "On an Inequality of Lieb and Thirring" Lett. Math. Phys.19. 167-170 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SAITO, Morihiko: "On b-Function, Spectrum and Rational Singularity" Preprint. RIMS-803. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] NARUKI, Isao: "On Smooth Quartic Embedding of Kummer Surfaces" Proc. Japan Acad.67. 223-225 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 河合 隆裕: "Secular Equations through the Exact WKB Analysis" Preprint RIMSー852. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 柏原 正樹: "On Crystal Bases of the qーAnalogue of Universal Enveloping Algebras" Duke Mathematical Journal. 63. 465-516 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 柏原 正樹: "Global Crystal Bases of Quantum Groups" Preprint RIMSー756. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 恭司: "A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces" Publ.RIMS,Kyoto Univ.27. 431-460 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 恭司: "On a Linear Structure of a Quotient Variety by a Finite Reflexion Group" Preprint RIMSー753. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 盛彦: "On bーFunction,Spectrum and Rational Singularity" Preprint RIMSー803. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 柏原 正樹: "Crystallizing the qーanalogue of Universal Envelping Algebras" Preprint,RIMSー728. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 三輪 哲二: "Braid Group Representations arising from the Generalized Chiral Potts Models" Preprint,RIMSー729. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 高崎 金久: "Analytic Expression of Voros Coefficients and its Application to WKB Connection Problem" Preprint,RIMSー725. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 恭司: "The Limit Element in the Configuration Algebra for a Discrete Group I" Preprint,RIMSー726. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 盛彦: "On the Injectivity of Cycle Maps" Preprint,RIMSー721. (1990)

    • Related Report
      1990 Annual Research Report

URL: 

Published: 1991-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi