國立清華大學 數學系

Abstract: 

The representation theory is a branch of algebra that studies the symmetries of mathematical and physical systems. The ultimate problem in representation theory is to classify and then understand the irreducible modules or their formal characters. Such a problem for Lie algebras of finite type over complex numbers was completely solved in the 80's à la the Kazhdan-Lusztig theory; while it remains wide open for modular representation theory over affine Lie algebras. In this talk, I will describe ideas and methods towards solving the irreducible character problem, as well as ongoing progress in the modular affine case.