Mini-course on representation theory of Lie algebras (I)~(IV)
Mr. Chun-Ju LaiUniversity of Virginia 下午3:00–5:00 Hongjing Hall 107 室Abstract:
The representation theory is a powerful tool that realizes problems in abstract algebra in the language of linear algebras. On one hand, it has ubiquitous applications, e.g., Fourier analysis, number theory, algebraic geometry, topology and mathematical physics. On the other hand, the approaches to representation theory are diverse, including methods from geometry, ring theory, combinatorics, topology and differential equations.
In this talk I will cover the following topics:
1. Introduction to representation theory.
2. Classification theorem of simple Lie algebras.
3. Weyl groups, Linkage principles and Kazhdan-Lusztig theory.
4. Categorification.
Prerequisites:
1. Linear algebra
2. Undergraduate algebra