two dimensional quantum field theory and representation theory

二维量子场论与表示论

• 批准号: 09304021
• 负责人: TSUCHIYA Akihiro
• 金额: $ 9.28万
• 依托单位: Nagoya University
• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304021/
• 关键词: Virasoro algebra; Affine Lie algebra; Conformal Field theory; Affine Hecke algebra; KZ方程式; 退化型双アファイン・ヘッケ環

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.

我们研究了退化双仿射Hecke代数H_N的表示，以表征在仿期lie代数的synmerties中，顶点算子的矩阵元素的空间用于保形场理论1。使用互动操作员，我们研究了由抛物线副总代词诱导的标准模块的结构。作为脱位仿射Hecke代数H_N模块2。我们定义了仿射lie代数SLM（C）的张量产品的高度空间f_n（a，b）上H_N模块的结构。这些表示是通过使用共形场理论的K-Z运算符与Cherednik-Dunkle运算符之间的关系来进行的。这些表示空间与共形场理论中的N点顶点操作员的空间有着深厚的关系。3。使用SLM的可集成模块的分辨率，我们构造了标准H_N模块的复合物，该模块的络合物将F_N（A，B）作为头4。使用H_N模块的交织算子，我们在f_n（a，b）中构造了s [e]的特征矢量。并结合了这些特征载体的H_n-invariant空间的字符。

项目成果

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

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。

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。

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。

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；