Abstract :

This event consists of two back-to-back expository talks with a fifteen-minute break in between. In the first session (2:30 PM - 3:30 PM), I will discuss the structure and representation theory of finite-dimensional simple Lie algebras, leading to the classification of their finite-dimensional irreducible representations.
In the second session (3:45 PM - 4:45 PM), I will move to the infinite-dimensional case, introducing the well-known Chari-Pressley classification of irreducible integrable representations of affine Lie algebras after laying the necessary groundwork. I will then introduce the concept of weakly integrable representations and provide a classification of irreducible weakly integrable representations, extending the Chari-Pressley result.