Quantum vertex algebras

该项目旨在解决与李代数相关的量子群族和顶点代数族的结构和表示的主要数学问题。量子群理论起源于统计力学中的可解晶格模型，它与数学和物理中的广泛学科有着重要的联系和应用。该项目将扩展和发展经典和量子版本的顶点代数的显式理论，这对共形场论和孤子自旋链模型是重要的。

The project aims to address major mathematical problems on the structure and representations of the families of quantum groups and vertex algebras associated with Lie algebras. Originating from solvable lattice models in statistical mechanics, the theory of quantum groups has important connections with, and applications to, a wide range of subjects in mathematics and physics. The project will extend and develop explicit theory of both the classical and quantum versions of the vertex algebras which are of importance to conformal field theory and soliton spin-chain models.