Extensions of Deformed W-algebras via qq-characters

We use combinatorics of qq-characters to study extensions of deformed W-algebras. We describe additional currents and part of the relations in the cases of \(\mathfrak {gl}(n|m)\) $\mathfrak{gl}(n|m)$ and \(\mathfrak {osp}(2|2n)\) $\mathfrak{osp}(2|2n)$ .