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Study of applied representation theory in global analysis

Research Project

Project/Area Number 09640105
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKyoto Institute of Technology

Principal Investigator

TSUKAMOTO Chiaki  Kyoto Inst.of Tech., Fac.of Textile Science, Associate Professor, 繊維学部, 助教授 (80155340)

Co-Investigator(Kenkyū-buntansha) YAGASAKI Tatsuhiko  Kyoto Inst.of Tech., Fac.of Eng. and Design, Associate Professor, 工芸学部, 助教授 (40191077)
OKURA Hiroyuki  Kyoto Inst.of Tech., Fac.of Eng. and Design, Associate Professor, 工芸学部, 助教授 (80135649)
MAITANI Fumio  Kyoto Inst.of Tech., Fac.of Eng. and Design, Professor, 工芸学部, 教授 (10029340)
NAKAOKA Akira  Kyoto Inst.of Tech., Fac.of Eng. and Design, Professor, 工芸学部, 教授 (90027920)
UCHIYAMA Jun  Kyoto Inst.of Tech., Fac.of Textile Science, Professor, 繊維学部, 教授 (70025401)
朝田 衛  京都工芸繊維大学, 工芸学部, 助教授 (30192462)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordsrepresentaion theory / analytic torsion / spectral zeta funcion / spectral geometry / 対称性 / ツォル変形 / 積分幾何学
Research Abstract

We have investigated the analytic torsion of line bundles over compact Hermitian symmetric spaces. The analytic torsion is defined as the first derivative at zero of the sum of spectral zeta functions derived from the spectral data of Hodge Laplacians.
We first showed that the lodge Laplacians of compact Hermitian symmetric spaces C/H is written by the Casimir operator of the group G of automorphisms, the Casimir operator of the isotropy group K, and the action of K on the fiber. Since these operators act by scalar multiplication on each irreducible G-submodules of the space of sections, we can determine the spectrum of Hodge Lapacian by studying the branching law of C-modules as K-modules, in view of Frobenius' reciprocity law. The muliplicity of each eigen value is computed by Weyl's formula.
We computed the spectral zeta functions associated with the product of the hyperplane section line bundle over complex projective space. These type of spectral zeta functions had been treated by Carletti and Monti-Bragadin. We refined their results on the Dirichlet series and succeeded in computing the analytic torsions for low dimensional projective spaces.
The similar method used in the computation of spectral data arc also applicable to the study of integrability of conformal infinitesimal Zoll deformations.
The other results by investigators are shown in the references.

Report

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

    (39 results)

All Other

All Publications (39 results)

  • [Publications] Jun Uchiyama: "On the Neumann and Wigner potentials" J.of Diff.Equations. (発表予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Exact Solution of Evolution Equation for Linear Viscoelastic Medium" Theoretical and Applied Mechanics(proceedings of the 46th J.N.C for applied mech.). 46. 95-108 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "An Analysis to Nonlinear Creep Behaviour of Viscoelastic Medium with Structure Changes by Means of Irreversible Thermodynamics" Theoretical and Applied Mechanics(proceedings of the 47th J.N.C for applied mech.). 47. 85-99 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "A Method of Wavelet Construction from n-MRA" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(発表予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Examples of Continuous and Compactly Supported Wavelets with Scaling Function Satisfying a Dilation Equation of Scale 3" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(発表予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Une Remarque sur la Formule de Stirling" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(発表予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Restoration of Lost Samples by Oversampling near the Nyquist Rate" Japan J.of industrial and applied Math.発表予定. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Fumio Maitani: "Conformal welding of annuli" Osaka J.Math.35. 579-591 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 米谷文男: "ベルグマン計量の調和変動による面のrigidityについて" 数理解析研究所講究録「短期共同研究 再生核の理論とその応用」. 1067. 169-175 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 米谷文男: "単葉有理系函数の線形結合の非単葉性について" 数理解析研究所講究録「短期共同研究 複素関数論の微分方程式への応用」. 1062. 128-139 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Fumio Maitani: "Moduli of ring domains obtained by a conformal welding" Kodai Math.J.20. 161-171 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 米谷文男: "極値截線写像の線形結合の単葉性について" 数理解析研究所講究録「短期共同研究Convolutionの新しい展開」. 1012. 56-65 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Jun Uchiyama: "On the von Neumann and Wigner potentials" J.of Diff.Equations. (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira nakaoka: "Exact Solutionof Evolution Equation for linear Vis-coelastic Medium" Theoretical and Applied Mechanics (proceedings of the 46th J.N.C for applied mech.). 46. 95-108 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "An Analysis to Nonlinear Creep Behavior of Vis-coelastic Medium with Structure Changes by Means of Irre-versible Thermodynamics" Theoretical and Applied Mechanics (proceedings of the 47th J.N.C for applied mech.). 47. 85-99 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "A Method of Wavelet Construction from n-MRA" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Examples of Continuous and Compactly Supported Wavelets with Scaling Function Satisfying a Dilation Equation of Scale 3" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Une Remarque sur la Formule de Stirling" Mem.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Akira Nakaoka: "Restoration of Lost Samples by Oversampling near the Nyquist Rate" Japan J.of industrial and applied Math.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Fumio Maitani: "Conformal welding of annuli" Osaka j.Math.35. 579-591 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Fumio Maitani: "Moduli of ring domains obtained by a conformal weld-ing" Kodai Math.J.20. 161-171 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroyuki Okura: "A new approach to the skew product of symmetric Markov processes" Mem.Fac.Eng.and Design Kyoto Inst.Tech. 46. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Infinite-dimensional manifold triples of homeo-morphism groups" Topology Appl.76. 261-281 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "PL approximations of fiber preserving homeo-morphisms of vector bundles" Tsukuba J.Math.21 (1). 181-198 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "The groups of quasiconformal homeomorphisms on Riemann surfaces" Proc.Amer.Math.Soc.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "Spaces of embeddings of compact polyhedra into 2-manifolds" Topology Appl.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tatsuhiko Yagasaki: "The homeomorphism groups of noncompact 2- manifolds" Mcm.of the Fac.of Eng.and Design Kyoto Inst.of Tech.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Jun Uchiyama: "On the von Neumann and Wigner potentials" J.of Diff.Equations. (発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akira Nakaoka: "Restoration of Lost Samples by Oversampling near the Nyquist Rate" Japan J.of industrial and applied Math.(発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Fumio Maitani: "Conformal welding of annuli" Osaka J.Math.35. 579-591 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroyuki Okura: "A new approach to the skew product of symmetric Markov processes" Mem.Fac.Eng.and Design Kyoto Inst.Tech.46. 1-12 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "The groups of quasiconformal homeomorphisms on Riemann surfaces" Proc.Amer.Math.Soc.(発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "Spaces of embeddings of compact polyhedra into 2-manifolds" Topology Appl.(発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 米谷文男: "極値截線写像の線形結合の単葉性について" 数理解析研究所講究録「短期共同研究Convolutioの新しい展開」. 1012. 56-65 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Nakaoka: "Exact solutions of evolution equation for linear viscoelastic medium" Theoretical and Applied Mechanics (Proc.of the 44th Japan Nat.Cong.for Appl.Mech.). 46. 95-108 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroyuki Okura: "A new approach to the skew product of symmetric Markov processes" Mem.Fac.Eng.and Design Kyoto Inst.Tech.(発表予定). 1-12 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "PL approximations of fiber preserving homeomorphisms of vector bundles" Tsukuba J.Math.21. 181-198 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tatsuhiko Yagasaki: "Infinite-dimensional manifold triples of homeomorphism groups" J.Topology Appl.76. 261-281 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Mamoru Asada: "On a family of linear representations associated with Galor's representations in the automorphism groups of pro-l fundamental groups" Memo.Engi.and Design Kyoto Inst.Tech.45. 1-8 (1997)

    • Related Report
      1997 Annual Research Report

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

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