\(W\)-algebras associated with centralizers in type \(A\)

A. I. Molev

Abstract

We introduce a new family of affine \(W\)-algebras associated with the centralizers of arbitrary nilpotent elements in \(\mathfrak{gl}_N\). We define them by using a version of the BRST complex of the quantum Drinfeld–Sokolov reduction. A family of free generators of the new algebras is produced in an explicit form. We also give an analogue of the Fateev–Lukyanov realization for these algebras by applying a Miura-type map.