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Vertex operator algebras with group action

Research Project

Project/Area Number 09640019
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHitotsubashi University

Principal Investigator

YAMADA Hiromichi  Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (50134888)

Co-Investigator(Kenkyū-buntansha) ISHIMURA Naoyuki  Hitotsubashi University, Graduate School of Economics, Assoc.Prof., 大学院・経済学研究科, 助教授 (80212934)
YAMAZAKI Masao  Hitotsubashi University, Graduate School of Economics, Assoc.Prof., 大学院・経済学研究科, 助教授 (20174659)
FUJITA Takahiko  Hitotsubashi University, Faculty of Commerce, Prof., 商学部, 教授 (50144316)
MACHIDA Hajime  Hitotsubashi University, Faculty of Commerce, Prof., 商学部, 教授 (40090534)
IWASAKI Shiro  Hitotsubashi University, Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (00001842)
永島 孝  一橋大学, 大学院・経済学研究科, 教授 (00017526)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsvertex operator algebra / Virasoro algebra / conformal element / finite group / simple module
Research Abstract

In 1997 a subalgebra having order three symmetry of a vertex operator algebra associated with a rank two root lattice of type A was discovered and its properties were studied. In particular its automorphism group was determined and its simple modules were classified. The results were written in a joint paper Ternary codes and vertex operator algebras. Relations between this vertex operator algebra and the Monster module still remain to be studied. Moreover, Borwein type identity was studied from a point of view of vertex operator algebra. The results were written in a joint paper Borwein identity and vertex opertor algebras.
In 1998 all highest weight vectors with weight at most two of a vertex operator algebra associated with a root lattice of type A were classified. Highest weight vectors are important, because once they are known then a vertex operator algebra can be decomposed into a direct sum of simple modules for a tensor product of Virasoro vertex operator algebras. Although not all highest weight vectors are known, much information about the structure of the vertex operator algebra can be obtained from highest weight vectors with weight at most two. For example, a vertex operator algebra having a symmetry of order 4 was constructed by using these highest weight vectors. Recently all highest weight vectors were classified in the case of rank three root lattice of type A.In order to generalize this result to a root lattice of arbitrary rank, a new idea would be required.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (61 results)

All Other

All Publications (61 results)

  • [Publications] Kitazume, M.: "Ternary codes and vertex operater algebras" J.Algebra. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Iwasaki, S.: "Infinite families of 2- and 3-designs with parameters ν=p+1, k=(p-1) 12^i+1, where p odd prime, 2^eT (p-1), e【greater than or equal】2, 1【less than or equal】i【less than " J.Comb, Designs. 5. 95-110 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Iwasaki, S.: "A remark on the action of PGL (2, q) and PSL (2, q) on the projective line" Hokkaido Math.J.26. 203-209 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Machida, H.: "The clone space as a metric space" Acta Applicandae Mathematicae. 52. 297-304 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Machida, H.: "Some continuous maps on the space of clones in multiple-valued logic" Proc.28th International Symp.on Multiple-Valued Logic. 374-379 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Rosenberg: "Gigantic pairs of minimal clones" Proc.29th International Symp.on Multipl-Valued Logic. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "The Navier-Stokes equation with distributions as initial data and application to self-similar solutions" Proc.Conf.New Trends in Microlocal Analysis. 125-141 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Representation formula, net force and energy relation to the stationary Navier-Stokes equations in 3-dimentional exterior domains" Kyushu J.Math.51. 239-260 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "The Cauchy problem in the Lorentz space for the Navier-Stokes equation in exterior domains" Proc.Fourth MSJ Int.Research Institute. 243-248 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Exterior problem for the stationary Navier-Stokes equations in the Lorentz space" Math.Ann.318. 279-305 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "On a large class of stable solutions to the Navier-Stokes equations in exterior domains" Math.Z.228. 751-785 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Exterior problem for the Navier-Stokes equations, existance, uniqueness and stability of stationary solutions" Proc.third Int.Conf.at Oberwolfach. 86-98 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Solutions for the Gauss curvature evolution of rotationally symmetric surface" Nonl.Anal.T.M.A.33. 97-104 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Shape of spirals" Tohoku Math.J.50. 197-202 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Asai, k.: "On the interior derivative blow-up for the curvature equation of capillary surfaces" Proc.Amer.Math.Soc.126. 835-840 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ikota, R.: "On the structure of steady solutions for the kinematic model of spiral waves in excitable media" Japan J.Indust.Appl.Math.15. 317-330 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Characterization on the long time behavior of the 2D Navier-Stokes equation" Pitman Research Notes Math.388. 38-44 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Remarks on the blow-up criterion for the 3D Boussinesq equations" Math.Models Meth.Appl.Sci.9. (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kitazume, M.: "Ternary codes and vertex operator algebras" J.Algebra. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Iwasaki, S.: "Infinite families of 2- and 3-designs with parameters nu=p+1, kappa=(p-1)/2^i+1, where p odd prime, 2^eT(p-1), e<greater than or equal>2,1<less than or equal>i<less than or " J.Comb.Designs. 5. 95-110 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Iawsaki, S.: "A remark on the action of PGL (2, q) and PSL (2, q) on the projective line" Hikkaido Math.J.26. 203-209 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Machida, H.: "The clone space as a metric space" Acta Applica.Math.52. 297-304 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Machida, H.: "Some continuous maps on the space of clones in multiple-valued logic" Proc.28th Int.Symp.on Multiple-Valued Logic. 374-379 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Rosenberg, I.G.: "Gigantic pairs of minimal clones" Proc.29th Int.Symp.on Multiple-Valued Logic. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "The Navier-Stokes equation with distributions as initial data and application to self-similar solutions" Proc.Conf., New Trends in Microlocal Analysis. 125-141 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Representation formula, net force and energy relation to the stationary Navier-Stokes equations in 3-dimensional exterior" Kyushu J.Math.51. 239-260 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "The Cauchy problem in the Lorentz space for the Navier-Stokes equation in exterior domains" GAKUTO Int.Ser.Math.Sci.Appl.10. 243-248 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Exterior problem for the stationary Navier-Stokes equations in the Lorentz space" Math.Ann.318. 279-305 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "On a larger class of stable solutions to the Navier-Stokes equations in exterior domains" Math.Z.228. 751-785 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kozono, H.: "Exterior problem for the Navier-Stokes equations, existence, uniqueness and stability of stationary solutions" Theory of the Navier-Stokes equations. 86-98 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Self-similar solutions for the Gauss curvature evolution of rotationally symmetric surfaces" Nonl.Anal.T.M.A.33. 97-104 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Shape of spirals" Tohoku Math.J.50. 197-202 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Asai, K.: "On the interior derivative blow-up for the curvature evolution of capillary surfaces" Proc.Amer.Math.Soc.126. 835-840 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ikota, R.: "On the structure of steady solutions for the kinematic model of spiral waves in excitable media 317-330,1998" Japan J.Indust.Appl.Math.15.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Characterization on the long time behavior of the 2D" Pitman Research Notes Math., Navier-Stokes equations. 388. 38-44 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishimura, N.: "Remarks on the blow-up criterion for the 3D Boussinesq equations" Math.Models Meth.Appl.Sci.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Imai, H.: "Mortion of spirals by crystalline curvature" Math.Model.Numer.Anal.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kitazume,M.: "Ternary codes and vertex operator algebras" J.,Algebra. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Iwasaki,S.: "Infinite families of 2- and 3-designs with parameters ν=p+1,k=(p-1)/2^i+1,where p odd prime,2^e T(p-1),e【greater than or equal】2,1【less than or equal】i【less than " J.Comb.Desighs. 5. 95-110 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Iwasaki,S.: "A remark on the action of PGL(2,q) and PSL(2,q) on the projective line" Hokkaido Math.J.26. 203-209 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Machida,H.: "The clone space as a metric space" Acta Applicandae Mathematicae. 52. 297-304 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Machida,H.: "Some continuous maps on the space of clones in maltiple-Valued logic" Proc.28th International Symp.on Multiple-Valned Logic. 374-379 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Rosenberg: "Gigantic pairs of minimal clones" Proc.29th International Symp.on Multiple-Valned Logic. (発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "The Navier-Stokes equation with distributions as initial data and application to self-similar solutions" Proc.Conf.New Trends in Microlocal Analysis. 125-141 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "Representation formula,net force and energy relation to the stationary Navier-Stokes equations in 3-dimentional exterior domains" Kyushu J.Math.51. 239-260 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "The Canchy problem in the Lorentz space for the Navier-Stokes eguation in exterior domains" Proc.Fourth MSJ Int.Research Institute. 243-248 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "Exterior problem for the stationary Navier-Stokes eguations in the Lorentz space" Math.Ann.318. 279-305 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "On a large class of stable solutions to the Navier-Stokes equations in exterior domains" Math.Z.228. 751-785 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kozono,H.: "Exterior problem for the Navier-Stokes equations,existance,unigueness and stability of stationary solutions" Proc.third Int.Conf.at Oberwolfach. 86-98 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ishimura,N.: "Solutions for the Gauss curvature evolution of rotationally symmetriesurface" Nonl.Anal.T.M.A.33. 97-104 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ishimura,N.: "Shape of spirals" Tohoku Math.J.50. 197-202 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Asai,K.: "On the interior derivative blow-up for the curvature equation of capillary surface" Proc.Amer.Math.Soc.126. 835-840 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ikota,R.: "On the structure of steady solutions for the kinematic model of spiral waves in excitable media" Japan J.Indust.Appl.Math.15. 317-330 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ishimura,N.: "Characterization on the long time behavior of the 2D Navier-Stokes equatio" Pitman Research Notes Math.388. 38-44 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ishimura,N.: "Remarks on the blow-up criterion for the 3D Boussinesq equations" Math.Models Meth.Appl.Sci.9(発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Kaneko,M: "Axiomatic indefinability of common knowledge in finitary logics" Epistemic logic and the theory of games and decisions. 69-93 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kozono,H: "Representation formula,net force and energy relation to the stationary Navier-Stokes equations in 3-dimensional exterior domains" Kyushu Journal of Mathematics. 51. 239-260 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kozono,H: "Exterior problem for the stationary Navier-Stokes equations in the Lorentz space" Mathematishe Annalen. 発表予定.

    • Related Report
      1997 Annual Research Report
  • [Publications] Ishimura,N: "Uniqueness for unbounded classical solutions of the MHD equations" Mathematical Meth.Appl.Sci.20. 617-623 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Ishimura,N: "Shape of spirals" Tohoku Mathematical Journal. 発表予定.

    • Related Report
      1997 Annual Research Report
  • [Publications] Ikota,R: "On the steady solutions for the kinematic model of spiral waves in excitable media" Japanese J.Indust.Appl.Math.発表予定.

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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