Résumé

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..

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