Deformed W-algebras are two-parameter deformations of classical W-algebras that exhibit deep connections with quantum integrable systems. A key feature of these algebraic structures is that their fields can be understood as deformations of ordinary q-characters, naturally leading to their designation as « qq-characters ». In the established theory, q-characters are inherently generated by the q-characters of fundamental representations. This structural property directly motivates the central question we will explore in this talk: How can we explicitly construct the corresponding « fundamental fields » within the deformed W-algebra ? To answer this question, we reformulate an algorithm inspired by the Frenkel-Mukhin algorithm and apply it to construct these fundamental fields..

https://indico.math.cnrs.fr/event/16460/