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1993 Fiscal Year Final Research Report Summary

Study of association schemes

Research Project

Project/Area Number 04452005
Research Category

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

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

Principal Investigator

BANNAI Eiichi  Kyushu Univ., Fac. of Science, Prof., 理学部, 教授 (10011652)

Co-Investigator(Kenkyū-buntansha) YOSHIDA Masaaki  Kyushu Univ., Fac. of Science, Prof., 理学部, 教授 (30030787)
SHIRATANI Katsumi  Kyushu Univ., Fac. of Science, Prof., 理学部, 教授 (80037168)
INOUE Junko  Kyushu Univ., Fac. of Science, Research Associate, 理学部, 助手 (40243886)
MUNEMASA Akihiro  Kyushu Univ., Fac. of Science, Research Associate, 理学部, 助手 (50219862)
YAMADA Mieko  Kyushu Univ., Fac. of Science, Associate Prof., 理学部, 助教授 (70130226)
Project Period (FY) 1992 – 1993
Keywordsalgebraic combinatorics / association scheme / link invariant / spin model / Bose-Mesner algebra / finite abelian group / modular invariance / Four-weight spin model
Research Abstract

The conceptof spin model was introduced by V.F.R.Jones in the paper published in Pac.J.Math. (1989). Each spin model gives a link invariant. The main research of the principal investigator in the last one year was in the following 2 directions. (1) Generalizing the concept of spin model and find such new spin models giving link invariants, (2) To study further spin models in connection with association schemes and releted object in algebraic combinatorics, then to study the construction and classfication problems of spin models in that framework. Explicit results are as follows. (1) In a joint work with Etsuko Bannai, we intriduced the concept of generalized generalized spin models (4-weighs spin models) by further generalizing the concept of generalized spin models introduced by Kawagoe-Munemasa-Watatani. We also constructed spin models on finitte cyclic groups by using the classification of the modular invariance properties on finite cyclic groups. (2) In a jouint work with Etsuko Bannai and F.Jaeger, we proved that the modular invariance holds if a generalized spin model generates the Bose-Mesner algebra of an association scheme, and we classified the modular invariance properties on finite abelian groups. We also proved that each such solution of the modular invariance gives a spin model on the abelian group, which generalizes the work of Kac and Wakimoto of the construction of spin models on abelian groups from an even Q-form. We also obtained the classification of small spin models in a joint work with F.Jaeger and A.Sali.

  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] 坂内英一: "代数的組合せ論-アソシエションスキームの最近の話題-" 数学. 45. 55-75 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai: "Association schemes and fusion algebras(an introduction)" J.of Algebraic Combinatorics. 2. 327-344 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Spin models on finite cyclic groups" J.of Algebraic Combinatorics. (accepted for publication).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Generalized generalized spin models(four-weight spin models)" Pac.J.Math.(accepted for publication).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Generalized spin models and association schemes" Mem.of Fac.Sci.Kyushu Univ.47. 397-409 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai,F.Jaeger and A.Sali: "Classification of small spin models" Kyushu J.Math.(accepted for publication).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Eiichi Bannai: "Association shemes and fusion alegebras (an introduction)" J.of Algebraic Combinatorics. 2. 327-344 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Spin models on finite cyclic groups" J.of Algebraic Combinatorics. accepted for publication.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Generalized generalized spin models (four-weight spin models)" Pac. J.Math. accepted for publication.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Eiichi Bannai and Etsuko Bannai: "Generalized spin models and association scheme" Mem. of Fac. Sci. Kyushu Univ.47. 397-409 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Eiichi Bannai, F.Jaeger and A.Sali: "Classification of small spin models" Kyushu J.Math.accepted for publication.

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

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Published: 1995-03-27  

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