In the previous talk, we revisited some general aspects of the representation theory of the Lie algebra $\mathrm{gl}(n)$ and used them as motivation to study Gelfand-Tsetlin modules via Drinfeld categories. In this seminar, we will take a step back to build a solid foundation before diving into Gelfand-Tsetlin modules. We will start by recalling key results from the classical representation theory of $\mathrm{sl}(2)$, ensuring that we have the necessary tools and intuition. With this groundwork in place, we will then explore how Gelfand-Tsetlin modules appear in this setting. If time allows, we will also look at some examples for $\mathrm{sl}(3)$.
 

The seminar will be followed by a coffee-break. 
O seminário será seguido de um coffee-break.