Extensions of deformed $W$-algebras via $qq$-characters

TL;DR

This paper explores the structure of deformed $W$-algebras using $qq$-characters, identifying new currents and relations for specific Lie superalgebras, advancing understanding of their algebraic extensions.

Contribution

It introduces new currents and relations in deformed $W$-algebras for $rak{gl}(n|m)$ and $rak{osp}(2|2n)$ using combinatorics of $qq$-characters.

Findings

Described additional currents in deformed $W$-algebras.

Identified relations for $rak{gl}(n|m)$ and $rak{osp}(2|2n)$ cases.

Enhanced understanding of algebraic extensions of deformed $W$-algebras.

Abstract

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 $\mathfrak{gl}(n|m)$ and $\mathfrak{osp}(2|2n)$.