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Spin Models and Distance-Regular Graphs

Research Project

Project/Area Number 14540010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Medical and Dental University

Principal Investigator

NOMURA Kazumasa  Tokyo Medical and Dental University, College of Liberal Arts and Sciences, Professor, 教養部, 教授 (40111645)

Co-Investigator(Kenkyū-buntansha) KIYOTA Masao  Tokyo Medical and Dental University, College of Liberal Arts and Sciences, Professor, 教養部, 教授 (50214911)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Keywordsspin model / association scheme / Bose-Mesner algebra / distance-regular graph / 1-homogeneous / Terwilliger algebra / Bose-Mesner 代数 / 1-homogeneous / Terwilliger 代数 / Base-Mesner代数
Research Abstract

Our purpose is to study properties of Bose-Mesner algebras which support spin models. We obtaind the following results:
(1) It was shown. that every Bose-Mesner algebra which supports a spin model 'should be strongly self-dual.
(2) We obtained some properties of real solutions of the modular invariance equation associated to spin models on distance-regular graphs.
(3) We characterized nonsymrnetric Hadamard models. This enables us to classify nonsymmetric spin models with small index.
(4) It was shown that every DRG supporting a spin model should be 1-homogeneous.
(5) We obtained an algebraic characterization of 1-homogeneous property.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] Kazumasa Nomura: "A property of solusions of modular invariance equations for distance-regular graphs"Kyushu Journal of Mathematics. 56. 53-57 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazumasa Nomura: "Spin models of index 2 and Hadmard models"Journal of Algebraic Combinatorics. 17. 5-17 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Brian Curitn, Kazumasa Nomura: "Homogeneity of a distance-regular graph which supports a spin model"Journal of Algebraic Combinatorics. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazumasa Nomura: "A property of solusions of modular invariance equatiohs for distance-regular graphs"Kyushu Journal of Math.. Vol.56. 53-57 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazumasa Nomura: "Spin models of index 2 and Hadmard models."J. Algebraic Combinatorics. vol.17. 5-17 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Brian Curtin, Kazumasa Nomura: "Homogeneity of a distance-regular graph which supports a spin model."J. Algebraic Combinatorics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kazumasa Nomura: "Spin models of index 2 and Hadmard models"Journal of Algebraic Combinatorics. 17. 5-17 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Brian Curtin, Kazumasa Nomura: "Homogeneity of a distance-regular graph which supports a spin model"Journal of Algebraic Combinatorics. to appear.

    • Related Report
      2003 Annual Research Report
  • [Publications] Kazumasa Nomura: "A property of salutions of modular invariance equations for distance-regular graphs"Kyushu J. Math. 56. 53-57 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kazumasa Nomura: "Spin models of index 2 and Hadamord models"J. Algebraic Combinatorics. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Masao Kiyota, M.Murai, T.Wada: "Rativnality of eigenvalues of Carton Matrices in finite groups"J. Algebra. 249. 110-119 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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