Recent development of special functins … an approach from the representation thery and the complex integrals

特殊函数的最新发展……一种来自表示和复积分的方法

基本信息

  • 批准号:
    15340003
  • 负责人:
  • 金额:
    $ 7.94万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
  • 财政年份:
    2003
  • 资助国家:
    日本
  • 起止时间:
    2003 至 2006
  • 项目状态:
    已结题

项目摘要

Mimachi realized an irreducible representation of the Iwahori-Hecke algebra on the twisted homology group associated with a Selberg type integral. It was first constructed in the context of conformal field theory by Tsuchiya-Kanie. Our construction is based on the study of the homology group under a resonant condition on the exponents of integrands. We stress the importance of the study of integrals under such a resonant condition to the study of hypergeometric type functions and spherical functions. Mimachi with H. Ochiai (Nagoya) and M.Yoshida (Kyushu) formulated the concept of visible cycles and invisible cycles, and determined the dimension of the spaces of visible cycles under a resonant condition in some examples.Mimachi with M.Yoshida calculated intersection numbers of twisted cycles associated with a Selberg type integral. It gives a natural interpretation of the coefficients of the four-point correlation function, in conformal field theory, calculated by Dotsenko-Fateev. This is an answer to a long standing problem of clarifying the meaning of such coefficients appearing in correlation functions. In higher dimensional cases, the Terada model (nonsingular model arising from the point configuration) plays an important role.Kurokawa with M.Wakayama (Kyushu) studied generalized zeta regularizations. It shows that a discrete version of intersection numbers of twisted cycles should be settled.Takata studied a q-hypergeometric series which appears as a factor of the n-colored Jones polynomial associated with a twisted knot or a torus knot and derived the A-polynomials associated with them.
Mimachi实现了Iwahori-Hecke代数在与Selberg型积分相关的扭曲同调群上的不可约表示。它最初是由土屋-Kanie在共形场论的背景下构建的。我们的构造是基于对被积函数的指数在共振条件下的同调群的研究。我们强调了在这种共振条件下研究积分对超几何型函数和球函数研究的重要性。Mimachi与H。Ochiai(名古屋)和M.Yoshida(九州)提出了可见圈和不可见圈的概念,并在一些例子中确定了共振条件下可见圈空间的维数。Mimachi和M.Yoshida计算了与Selberg型积分相关的扭曲圈的相交数。它给出了一个自然的解释系数的四点相关函数,在共形场理论,计算Dotsenko-Fateev。这是一个长期存在的问题,澄清相关函数中出现的这些系数的含义的答案。在高维情形下,Terada模型(由点构型产生的非奇异模型)起着重要作用。Kurokawa和M.和歌山(九州)研究了广义zeta正则化。Takata研究了与扭纽结或环面纽结相关的作为n色Jones多项式因子的q-超几何级数,导出了与扭纽结或环面纽结相关的A-多项式。

项目成果

期刊论文数量(33)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Zeta regularized product expansion for multiple trigonometric functions
Zeta 正则化多项三角函数的乘积展开
  • DOI:
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    N.Kurokawa;M.Wakayama
  • 通讯作者:
    M.Wakayama
Reshetikhin-Turaev invariants of Seifert-manifolds for classical simple Lie algebras
经典简单李代数的 Seifert 流形的 Reshetikhin-Turaev 不变量
A generalization of the beta integral arising from the Knizhnik-Zamolodchikov equation for the vector representations of types B n, C n and D n
由 Knizhnik-Zamolodchikov 方程产生的 beta 积分的推广,用于 B n、C n 和 D n 类型的向量表示
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    K.Mimachi;T.Takamuki
  • 通讯作者:
    T.Takamuki
Intersection theory for loaded cycles IV-resonant cases
加载循环 IV 谐振情况的相交理论
  • DOI:
  • 发表时间:
    2003
  • 期刊:
  • 影响因子:
    0
  • 作者:
    K.Mimachi;H.Ochiai;M.Yoshida
  • 通讯作者:
    M.Yoshida
K.Mimachi, M.Yoshida: "Intersection numbers of twisted cycles associated with the Selberg integral and an application to the conformal field theory"Commun.Match.Phys.. (to appear).
K.Mimachi、M.Yoshida:“与 Selberg 积分相关的扭曲循环的交点数及其在共形场论中的应用”Commun.Match.Phys..(即将出现)。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
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MIMACHI Katsuhisa其他文献

MIMACHI Katsuhisa的其他文献

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{{ truncateString('MIMACHI Katsuhisa', 18)}}的其他基金

Recent development of special functions from the viewpoint of representation theory and integrals of complex variables
从表示论和复变积分的角度看特殊函数的最新发展
  • 批准号:
    19340004
  • 财政年份:
    2007
  • 资助金额:
    $ 7.94万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Recent development of special functios ----an approach from the representation thery and the complex integrals
特殊函数的最新发展----从表示论和复积分出发的方法
  • 批准号:
    12440010
  • 财政年份:
    2000
  • 资助金额:
    $ 7.94万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Modern development of special functions - approach from the representation theory and the integrals
特殊函数的现代发展 - 来自表示论和积分的方法
  • 批准号:
    09440020
  • 财政年份:
    1997
  • 资助金额:
    $ 7.94万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

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高维Erdelyi循环及其交数角度的超几何函数连接问题
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    19K03517
  • 财政年份:
    2019
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Shimura 曲线和模曲线上测地线的交点数。
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RUI: Complex Structures, Hyperbolic Invariants, Infinitesimal Currents and Intersection Numbers for Deformation Spaces
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  • 批准号:
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枚举代​​数几何中的交点数
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