本项目将在青年科学基金项目关于parafermion顶点算子代数的结构和表示的前期研究基础上进一步研究仿射李代数的可积最高权模决定的parafermion顶点算子代数的有理性及不可约模的分类; 确定B_n, C_n, F_4型仿射李代数的可积最高权模决定的parafermion顶点算子代数的自同构群. 研究高维仿射李代数等无穷维李代数的顶点算子表示问题及这些李代数与顶点算子代数的联系. 还将研究以交错环面为坐标代数的高维仿射李代数的权空间有限维的不可约可积模的分类和构造问题. 这些问题的解决既丰富了顶点代数理论, 又为研究高维仿射李代数等无穷维李代数的结构及表示提供一个有效的工具, 同时也将丰富高维共形场理论的研究.

On the basis of the National Natural Science Foundation for Youths, we will go on to study the rationality and the classification of irreducible modules of parefermion vertex operator algebras associated to integrable highest weight modules for any affine Kac-Moody algebra; determine the automorphism groups of parefermion vertex operator algebras associated to integrable highest weight modules for affine Kac-Moody algebras of type B_n, C_n and F_4. And we will study the vertex operator representations of extended affine Lie algebras and some other infinite dimensional Lie algebras, and moreover, the relationship between these Lie algebras and vertex operator algebras. We will also study the classification problem of irreducible integrable modules for the extended affine Lie algebras with alternative tori as coordinate algebra. Solving these problem will enrich the theory of vertex algebras, and provide an efficient tool for the structure and representation theory of extended affine Lie algebras, and at the same time, will enrich the study of high-dimensional conformal field theory.