We will first review the McKay correspondence and its generalization using elementary group theory. It gives a 1-1 correspondence between finite subgroups of SL(2, C) and simply laced affine Dynkin diagrams. We use group theoretical data to construct the basic representations of simply laced toroidal Lie algebras, which contain affine Lie algebras as distonguished subalgebras.

Speaker Biography: Professor Naihuan Jing

Professor Naihuan Jing is a professor at North Carolina State University, USA. He has been the recipient of numerous prestigious honors, including China's National Science Fund for Distinguished Young Scholars (Overseas), Germany's Alexander von Humboldt Research Fellowship, and the U.S. Fulbright Scholar Grant.

He has held academic and research positions at several world-renowned institutions, such as the Institute for Advanced Study in Princeton, the University of Michigan, and the University of Kansas. He has also visited and collaborated extensively as a guest professor or researcher at leading mathematical centers, including the Mathematical Sciences Research Institute (MSRI) in Berkeley, the Max Planck Institute for Mathematics in Bonn, and the Max Planck Institute for Mathematics in the Sciences in Leipzig.

His primary research interests encompass infinite-dimensional Lie algebras, quantum groups, vertex operator algebras, algebraic combinatorics, and quantum computation.