two dimensional quantum field theory and representation theory

点击翻译按钮获取中文摘要

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.