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Studies of Algebraic and Analytic Varieties

Research Project

Project/Area Number 02452003
Research Category

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

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyoto University

Principal Investigator

SAITO Kyoji  Kyoto University, Research Institute for Mathematical Sciences, professor, 数理解析研究所, 教授 (20012445)

Co-Investigator(Kenkyū-buntansha) MIWA Tetsuji  Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (10027386)
KAWAI Takahiro  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
NARUKI Isao  Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (90027376)
SAITO Morihiko  Kyoto University, Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (10186968)
KASHIWARA Masaki  Kyoto University, Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (60027381)
大沢 健夫  京都大学数理解析研究所, 助教授 (30115802)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥5,100,000 (Direct Cost: ¥5,100,000)
Fiscal Year 1991: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1990: ¥2,800,000 (Direct Cost: ¥2,800,000)
KeywordsTeichmuller Space / Modular Function / Quantum Group / Vertex Operator / K3 Surface / Hodge Module / WKB Theory / BRS Cohomology / moduli空間 / Teichmu^^¨ller空間 / configuration空間 / 数理物理学 / Hodge構造 / L^2ーcohomology
Research Abstract

Kyoji Saito has described the Teichmuller space for compact Riemann surfaces as the real point variety of affine algebraic scheme defined over Z, whose complex structure is described by an infinite sequence of local systems by generalizing the Eichler integrals. Then certain global automorphic form on the space is introduced by a limit element in the configuration Hopf algebra for the discrete group.
Masaki Kashiwara has developed a general frame of bases of quantum groups for the value q = 0 and called it crystal basis. Then together with Tetsuji Miwa and others, he showed that the crystal basis is equivalent to the pathes appeared in one point function for a solvable lattice model. In particular, for the vertex model they established that the one point function becomes character.
Morihiko Saito has developed a theory of Hodge module by a use of D-module theory as analogous of the solution of Weil conjecture due to Delinge. Then he gave its several georhetric applications such as a study of b-functions for non-isolated singulaxities and Dimca's conjecture on polynomial maps.
Isao Naruki has shown that abelian surfaces without a principal polarization but with a polarization by a Pfaffian of degree 3 admits that associated Kummer surface can be embedded into P^3 as a quartic surface.
Takahiro Kawai, together with Takashi Aoki and Yoshitsugu Takei, has given a micro local analytic foundation for the WKB method and Borel transformation. Then gave normal forms for the case of a few simple turning point and make it clear that some strange phenomenon in higher order equation based on certain intersection points.
Noboru Nakanishi, together with Izumi Ojima, gave a consistent formulation of local gauge invariance and BRS cohomology in the frame of relativistic quantum theory with indefinite metric and clarified their natural meanings.
Huzihiro Araki has generalized the Lieb Thirring inequality on the true of powers of positive self adjoint operators.

Report

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

    (24 results)

All Other

All Publications (24 results)

  • [Publications] 斎藤 恭司: "A Generalization of Eichler Integrals and Certain Local Systems over Spin Riemann Surfaces" Publ.RIMS,Kyoto University. 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.1990. 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] 斎藤 恭司: "The Limit Element in the configuration Algebra for a Discrete Group" RIMS preprint. 726. (1990)

    • 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: "On a linear structure of a quotient by a finite reflexion group" RIMS preprint. 753. (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analoque of universal enveloping algebras" Duke Math.J.,. 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: "Grobal Crystal Bases of Quantum Groups" RIMS Preprint. 756. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] SAITO, Khoji: "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.Springer-Verlag. 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: "The Limit Element in the Configurations Algebra for a Discrete Group" RIMS preprint. 726. (1990)

    • 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 by a finite reflexion group" RIMS preprint. 753. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] KASHIWAEA, Masaki: "On crystal bases of the q-analogue of universal enveloping algebras" Duke Math. J.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" RIMS preprint. 756. (1991)

    • Description
      「研究成果報告書概要(欧文)」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 University. 27. 431-460 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 恭司: "The Limit Element in the Configuration Algebra for a Discrete Group(A precis)" Proc.Int.Congr.Math.1990. 931-942 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 恭司: "The Limit Element in the Configuration Algebra for a Discrete Group" RIMS preprint. 726. (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] 斎藤 恭司: "On a linear structure of a quotient by a finite reflexion group" RIMS preprint. 753. (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 Math.J.63. 465-516 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 柏原 正樹: "Global Crystal Bases of Quantum Groups" RIMS preprint. 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" to appear in Publ.RIMS,Kyoto University. 27. (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 恭司: "Extended Affine Root Systems II" Publ.RIMS,Kyoto University. 26. 15-78 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 柏原 正樹: "Crystallizing the qーanalogue of universal enveloping algebras" Commun.Math.Phys.133. 249-260 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 盛彦: "Mixed Hodge Modules" Publ.RIMS,Kyoto University. 26. 221-333 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 盛彦: "DーModules on analytic spaces" Publ.RIMS,Kyoto University. 27. 291-332 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 大沢 健夫: "On the L^2 cohomology groups of isolated singularities" Adv.Stud.in Pure Math.

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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