## $$W$$-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.

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 Thursday, February 6, 2020