two dimensional quantum field theory and representation theory

二维量子场论与表示论

基本信息

  • 批准号:
    09304021
  • 负责人:
  • 金额:
    $ 9.28万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
  • 财政年份:
    1997
  • 资助国家:
    日本
  • 起止时间:
    1997 至 1998
  • 项目状态:
    已结题

项目摘要

We studied the representions of degenerate double affine Hecke algebra H_N to characterize the space of matrix elements of vertex operators for conformal field theory under the synmetries of affine Lie algebras.1. Using the intertwing operators, we studied the structure of the standard modules induced by the parabolic subalgebras. We get condition for irreduciblity and deconposition as degenerate affine Hecke algebra H_N modules.2. We defined structure of H_N-module on quatient spaces F_N (A, B) of tensor products of representation spaces of affine Lie algebra Slm (C) . These representations are defind by using relation between K-Z operators of conformal field theory and Cherednik-Dunkle operators. And these representation spaces have deep relationship to the space of N-points vertex operaters in the conformal field theory.3. Using the resolution of integrable modules of slm, we construct the complexes of standard H_N modules which has F_N (A, B) as the head.4. Using the intertwining operators of H_N-module, we construct eigen vectors of S [E] in the F_N (A, B) .And conpute the characters of H_N-invariant space of these eigen vectors.
研究了简并二重仿射Hecke代数H_N的表示,在仿射李代数的对称下刻画了共形场论顶点算子的矩阵元素空间。利用缠结算子,研究了抛物子代数诱导的标准模的结构。得到了简并仿射Hecke代数H_N模的不可约性和分解的条件。在仿射李代数Slm (C)的表示空间的张量积的象限空间F_N (A, B)上定义了h_n模的结构。利用共形场论的K-Z算子与Cherednik-Dunkle算子之间的关系定义了这些表示。这些表示空间与共形场论中的n点顶点算子空间有着深刻的关系。利用slm可积模的解析,构造了以F_N (A, B)为头的标准H_N模的复形。利用h_n模的缠结算子,构造了S [E]在F_N (A, B)中的特征向量。并计算这些特征向量在h_n不变空间中的特征。

项目成果

期刊论文数量(18)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
T.Arakawa,T.Suzuki and A.Tsuchiya: "Degenerate double affine Hecke algebras and conformal field theory" Topological Field Theory,Primitive Forms and Related Topics:the pro-ceedings of the 38^<th> Taniguchi symposium,Ed.M.Kashiwara et al.,. 1-34 (1998)
T.Arakawa、T.Suzuki 和 A.Tsuchiya:“退化双仿射 Hecke 代数和共形场论”拓扑场论、本原形式及相关主题:第 38 届谷口研讨会论文集,Ed.M
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    0
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A.N.Kirillov, A.Kuniba and T.Nakanish: "Skew Young diagram method in spectral decomposition of integrable lattice models II : Higher levels" Nucl.Phys.B529. 611-638 (1998)
A.N.Kirillov、A.Kuniba 和 T.Nakanish:“可积晶格模型谱分解中的斜杨图方法 II:更高水平”Nucl.Phys.B529。
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    0
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K.Aomoto: "Derivation of q-difference equations from connection matrix for Selberg type Jackson integrals" Jour.Difference Eq.and Its Appli.4. 247-278 (1998)
K.Aomoto:“从 Selberg 型 Jackson 积分的连接矩阵导出 q 差分方程”Jour.Difference Eq.and Its Appli.4。
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    0
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K.Aomoto: "On elliptic product formulas for Jackson integrals associated with reduced root systems" Jour.Alg.Comb.8. 115-126 (1998)
K.Aomoto:“关于与简化根系统相关的 Jackson 积分的椭圆乘积公式”Jour.Alg.Comb.8。
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    0
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T.Arakawa,T.Suzuki and A.Tsuchiya: "Degenerate double affine Hecke algebras and conformal field theory" Topological Field Theory,Primitive Forms and Related Topics ; the pro-ceedings of the 38^<th> Taniguchi symposium,Ed.M.Kashiwara et al.,. 1-34 (1998)
T.Arakawa、T.Suzuki 和 A.Tsuchiya:《退化双仿射 Hecke 代数和共形场论》拓扑场论、本原形式及相关主题;
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    0
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TSUCHIYA Akihiro其他文献

TSUCHIYA Akihiro的其他文献

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{{ truncateString('TSUCHIYA Akihiro', 18)}}的其他基金

Study of Promoting dialogue System between Victims/Bereaved families and Responsible party
促进受害人/家属与责任方对话制度的研究
  • 批准号:
    15K12965
  • 财政年份:
    2015
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Challenging Exploratory Research
Construction of Conformal field theory based on Representation theory of Vertex Operator Algebra
基于顶点算子代数表示论的共形域论构建
  • 批准号:
    22540010
  • 财政年份:
    2010
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
A Study of Transformation of School Conflict and Construction of Education ADR in Education System Reform Period
教育体制改革时期学校冲突转化与教育ADR构建研究
  • 批准号:
    22730003
  • 财政年份:
    2010
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
A Sociolegal Study for Construction of School Dispute Resolution Systems
学校纠纷解决体系构建的社会法学研究
  • 批准号:
    19730005
  • 财政年份:
    2007
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
On the study of two dimensional quantum field theory by the methodof representation theory
论用表示论方法研究二维量子场论
  • 批准号:
    18540078
  • 财政年份:
    2006
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Representation Theoretic Study of Two Dimensional Quantum Field Theory
二维量子场论的表示理论研究
  • 批准号:
    14204003
  • 财政年份:
    2002
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Representation Theoretic Study of Two Dimensional Quantum Field Theory
二维量子场论的表示理论研究
  • 批准号:
    11440020
  • 财政年份:
    1999
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

相似海外基金

Affine Lie algebra characters and Bethe Ansatz
仿射李代数字符和 Bethe Ansatz
  • 批准号:
    11640027
  • 财政年份:
    1999
  • 资助金额:
    $ 9.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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