Within the Theory of Gelfand-Tsetlin modules, the Drinfeld Categories were introduced in 2017 by V. Futorny et al. to demonstrate that every irreducible 1-singular Gelfand-Tsetlin module is isomorphic to a subquotient of the Universal 1-singular module.
The authors also noted that these categories could extend the classification of Gelfand-Tsetlin sl(n)-modules, which, at the time, was known only for sl(3).
These categories have proven to be a useful pictorial tool for understanding the behavior of Gelfand-Tsetlin sl(3)-modules described by V. Futorny et al.
In this talk, we provide a brief introduction to Gelfand-Tsetlin modules and Drinfeld categories. Our goal is to understand the construction of the Drinfeld quivers for simpler cases, specifically for sl(2)-modules and Generic Gelfand-Tsetlin sl(3)-modules. We will also demonstrate how these quivers describe the structure of the universal Gelfand-Tsetlin modules in each case.