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1992 Fiscal Year Final Research Report Summary

Study of Mathematical Sciences by Algebraic Methods

Research Project

Project/Area Number 03302001
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionTOHOKU UNIVERSITY

Principal Investigator

HOTTA Ryoshi  Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (70028190)

Co-Investigator(Kenkyū-buntansha) TANISAKI Toshiyuki  Hiroshima U.Fac.Sci.,Professor, 理学部, 教授 (70142916)
KAWANAKA Noriaki  Osaka U.Fac.Sci.,Professor, 理学部, 教授 (10028219)
MIWA Tetsuji  Kyoto U.RIMS,Professor, 数理解析研, 教授 (10027386)
MORITA Yasuo  Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (20011653)
ODA Tadao  Tohoku U.Fac.Sci.,Professor, 理学部, 教授 (60022555)
Project Period (FY) 1991 – 1992
KeywordsInvariant Theory / Duality / Quantum Groups / Algebraic Groups / Moduli of Vector Bundles / Hypergeometric Differential Equations / Conformal Fields / Number Theory
Research Abstract

The following conferences are organized and/or supported according to the main point of this project: 1.Symposium of Algebraic Geometry(1991.10.1-4,Kyoto Univ.) 2.New Trend of Invariant Theory(1991.12.16-18,Osaka Univ.) 3.Duality as Phenomenon(1992.8.4-6,Hakodate) 4.Quantum Groups and Related Topics(1992.10.3-5,Nagoya Univ.) 5.Representations of Algebraic Groups(1992.10.29-31,Tohoku Univ.)
The details are in the separated booklet "Report of the Results of the Project" and here is only a summary.
In Conf.1, the structure of moduli of vector bundles, which is also interested in mathematical physics, was a main topic and many related results were reported.
Conf.2 was organized by the head investigator and some of the others. There we tried to investigate the role of invariant theory, one of the main themes of classical algebra, in the modern analysis including mathematical physics. Varieties of topics were hypergeometric differential equations, representations of quantum groups, and conformal field theory.
Conf.3 is rather an unusual meeting where distinguished mathematicians of quite varieties of fields attended and discussed the concept "Duality" in mathematics (and even outer world). Many problems and results were proposed from number theory to physics. The proceedings will be soon published by the organizers.
For Conf.4, we supported the publication of its proceedings.
Conf.5 is for discussions of recent results and problems in somewhat traditional representation theory. Together with three foreign experts as participants,many results were reported including their technical points.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] R.Hotta: "Equisariant D-modules" Proc.ICPAM Wuhan Spring School. (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Oda: "The algolraic de Rham theorem for foric uarieties" Thohku Math.J.(1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Morita: "Distrilvtion of rational points on hyper-elliqtic surfaces" Tohoku Math.J.44. 345-358 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Miwa: "Corner transfer matrices and quantum affine algelras" Int.J.Modern Phys.A7. 279-302 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Kawanaka: "On sulfialcl symmetric spaces over a finete held" Osaka J.math. 28. 759-791 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Tanisaki: "Killing forms,Harich-Chandra isomoyhigms and universal R-matrices for quantum algelras" Int.J.Modern Phys. A7. 941-961 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Hotta: "Equivariant D-modules" Proc.ICPAM Wuhan Spring School. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Oda: "The algebraic de Rham Theorem for toric varieties" Tohoku Math.J.(1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Morita: "Distribution for rational points on hyper-elliptic surfaces" Tohoku Math.J.44. 345-358 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Miwa: "Corner transfer matrices and quantum affire algebras" Int.J.Modera Phys.A7. 279-302 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Kawanaka: "On subfield symmetric spaces over a finite field" Osaka J.Math.28. 759-791 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Tanisaki: "Killing forms,Harish-Chandra isomonphisms and universal R-matrices for quantum algebras" Int.J.Modern.Phys.A7. 941-961 (1992)

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

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Published: 1994-03-24  

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