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Moduli space of pointecl autrves and conismal field theory

Research Project

Project/Area Number 16340007
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

NAGATOMO Kiyokazu  Osaka University, Graduate School of Information Science and Technology, Associate Professor (90172543)

Co-Investigator(Kenkyū-buntansha) KANEKO Masanobu  Kyushu University, Faculty of Mathematics, Professor (70202017)
MATSUMURA Akitaka  Osaka University, Graduate School of Information Scienoe and Technology, Professor (60115938)
MIYAMOTO Masahiko  University of Tbukuba, Institute of Mathematics, Professor (30125356)
KOGA Yoshiyuki  Fukui University, Faculty of Engineering, associate Professor (20338429)
YAMANE Hiroyuki  Osaka University, Graduate School of animation Scienoe and Technology, Associate Professor (10230517)
伊達 悦朗  大阪大学, 大学院情報科学研究科, 教授 (00107062)
土屋 昭博  名古屋大学, 大学院・多元数理科学研究科, 教授 (90022673)
松尾 厚  東京大学, 大学院・数理科学研究科, 助教授 (20238968)
落合 啓之  名古屋大学, 大学院・多元数理科学研究科, 助教授 (90214163)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥17,500,000 (Direct Cost: ¥16,300,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2007: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2006: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2005: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2004: ¥4,300,000 (Direct Cost: ¥4,300,000)
KeywordsConformal field Theory / Pointed Riemann surface / Moduli space / Modular tensor category / 点付きリーマン面 / リーマン面 / 位相不変量 / テンソル圏 / D-加群 / 無限次元代数 / 表現論 / カイラル代数 / 頂点作用素代数 / Verlinde公式
Research Abstract

During 2005 and 2007 we studied moduli space of pointed Riemann surfaces and conformal field theory over them. We first studied vertex operator algebras and when VOA has Zhut's finiteness condition we established representation theory. This allows is construct conformal filed over the projective line. Given pointed Riemann surface we are able to define current Lie algebra from vertex operator algebra. Further using current Lie algebra we introduce a notion of sheaf of coinvariants, Under the condition of Zhu fibers of sheaf of coinvariants are finite dimensional This means that we obtain coherent sheaves. Moreover there sheaves axe equipped with flat connections which come from the action of Virasoro algebra. These imply that these sheaves are locally free. Next for rational vertex operator algebra with Zhu's condition case we are able to prove so-called factorization property for he ease of projective line ,i.e., any n point sheaves of coinvariants are expressed by 3 point sheave if n-s greater than 4.
On the other hand we have studied non-rational vertex operator algebra. For instance, W-algebra is an example such object Since W-algebm is not completely reducible, we have to classify indecomposable module. Now the list of indecomposable module is proposed and these modules are expected to be projective modules. If these are proved Ext* group will be completely determined. W-algebra is determined by positive integer p>1. When P=2 the category of modules of W-algebra is equivalent to the category of finite dimensional module for the restricted quantum group Uq(sl(2))q=1. In this research project we have constructed invariants of knots. Behind this successful work there is the fact that the category of finite dimensional restricted quantum group is ribbon category.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (29 results)

All 2007 2006 2005 2004 Other

All Journal Article (27 results) (of which Peer Reviewed: 5 results) Presentation (2 results)

  • [Journal Article] On ordinary primes for modular forms and the theta operator with M. Kaneko2007

    • Author(s)
      M, Chida
    • Journal Title

      Proc. Amer. Math. Soc. 135

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Representations of a Z/3Z-quantum group2007

    • Author(s)
      H. Yamane
    • Journal Title

      Pub1. RIMS, Kyoto Univ. 43

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On ordinary primes for modular forms and the theta operator with M Kaneko2007

    • Author(s)
      M, Chida
    • Journal Title

      Proc. Amer. Math. Soc 135

      Pages: 1001-1005

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Representations of a Z/3Z-quantum group2007

    • Author(s)
      H., Yamane
    • Journal Title

      Publ. RIMS, Kyoto Univ 43

      Pages: 75-93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Large-time Behavior of Solutions to an Initial-boundary Value problem on the Half Line for Scalar Viscous Conservation Law with A. Matsumura2007

    • Author(s)
      I. Hashimoto
    • Journal Title

      Met. Appl. Anal. 14

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations of a Z/3Z-quantum group2007

    • Author(s)
      H. Yamane
    • Journal Title

      Publ. RIMS, Kyoto Univ. 43

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On modular forms of weight (6n+1)/5 satisfying a certain differential equation2006

    • Author(s)
      Kaneko, M.
    • Journal Title

      Number Thoery---Tradition and Modernization

      Pages: 97-102

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Derivation and double shuffle relations for multiple zeta values2006

    • Author(s)
      Ihara, K
    • Journal Title

      Compositio Math. 142-02

      Pages: 307-338

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The structure of pre-Verma modules over the N=1 Ramond algebra2006

    • Author(s)
      K.Iohara
    • Journal Title

      Lett. Math. Phys 78

      Pages: 89-96

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Tilting equivalence for superconformal algebras2006

    • Author(s)
      K.Iohara
    • Journal Title

      Math. Scand 99

      Pages: 89-89

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence and stability of steady-state of one-dimensional quantum Euler-Poisson system for semiconductors2006

    • Author(s)
      H.Li
    • Journal Title

      J. Differential Equations 225・1

      Pages: 1-25

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The relaxation-time limit in the quantum hydrodynamic equations for semiconductors2006

    • Author(s)
      Ansgar Junge
    • Journal Title

      J. Differential Equations 225・2

      Pages: 440-464

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations2006

    • Author(s)
      F.Huang
    • Journal Title

      Archive for Rational Mechanics and Analysis 179・1

      Pages: 55-77

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Double zeta values and modular forms2006

    • Author(s)
      H.Gangl
    • Journal Title

      "Automorphic forms and Zeta functions",Proceedings of the Conference in Memory of Tsuneo Arakawa, World Scientific

      Pages: 71-106

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Conformal field theories associated to regular chiral vertex operator algebras I: theories over the projective line with A. Tsuchiya2005

    • Author(s)
      K. Nagatomo
    • Journal Title

      Duke Math. J. 128

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Conformal field theories associated to regular chiral vertex operator algebras I : theories over the projective line with A.Tsuchiya2005

    • Author(s)
      K., Nagatomo
    • Journal Title

      Duke Math. J 128

      Pages: 393-471

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Conformal field theories associated to regular chiral vertex operator algebras I : theories over the projective line2005

    • Author(s)
      K.Nagatomo
    • Journal Title

      Duke Mathematical Journal 128・3

      Pages: 393-471

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Sharp lower bound for the lifespan of systems of semilinear wave equations with multiple speeds2005

    • Author(s)
      S.Katayama
    • Journal Title

      J.Math.Kyoto University 45・2

      Pages: 391-403

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the local factor of the zeta function of quadratic orders2005

    • Author(s)
      M.Kaneko
    • Journal Title

      Zeta functions, Topology, and Quantum Physics, Developments in Mathematics (Springer) 14

      Pages: 75-79

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 3-transposition groups of symplectic type and vertex operator algebras2005

    • Author(s)
      A.Matsuo
    • Journal Title

      Journal of Mathematical Society of Japan 57・3

      Pages: 639-649

    • NAID

      10017177680

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Second Homology of Lie Superalgebras2005

    • Author(s)
      K.Iohara
    • Journal Title

      Math.Nach. 278・9

      Pages: 1041-1053

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A new construction of the Moonshine vertex operator algebra over the real number field2004

    • Author(s)
      Masahiko Miyamoto
    • Journal Title

      Ann.of Math. 159・2

      Pages: 535-596

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Polynomials associated with the hypergeometric functions with finite monodromy group2004

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      Intern.J.Math. 15

      Pages: 629-649

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Representation theory of N=2 super Virasoro algebra : Twisted sector2004

    • Author(s)
      Kenji Iohara
    • Journal Title

      Journ.Funct.Anal. 214・2

      Pages: 450-518

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Serre-type theorem for the elliptic Lie algebras with rank 22004

    • Author(s)
      Hiroyuki Yamane
    • Journal Title

      Publ.RIMS, Kyoto Univ. 40

      Pages: 441-469

    • NAID

      130003585560

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Conformal field theories associated to regular chiral vertex operator algebras I : theories over the projective line

    • Author(s)
      Kiyokazu Nagatomo
    • Journal Title

      Duke Math.Journal (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the local factor of the zeta function of quadratic orders

    • Author(s)
      Masanobu Kaneko
    • Journal Title

      Zeta functions, Topology and Quantum Physics (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Presentation] 単独粘性保存則に対する半直線上のある初期値境界値問題について,橋本伊都子との共同講演2007

    • Author(s)
      松村昭孝
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] On an initial boundary value problem to scalar viscous conservation law on the on half line2007

    • Author(s)
      Matsumura, Akitaka
    • Organizer
      meeting of Japanese Mathematical Society
    • Place of Presentation
      Tohoku University
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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