two dimensional quantum field theory and representation theory

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。

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.