$W$-algebras associated with centralizers in type $A$

TL;DR

This paper introduces a new family of affine W-algebras linked to centralizers of nilpotent elements in gl_N, constructed via BRST complex and quantum Drinfeld--Sokolov reduction, with explicit generators and a Miura-type realization.

Contribution

It defines novel affine W-algebras associated with arbitrary nilpotent centralizers in gl_N, providing explicit generators and a Miura-type realization.

Findings

Explicit free generators of the new W-algebras are constructed.

An analogue of the Fateev--Lukyanov realization is established.

The algebras are associated with centralizers of nilpotent elements in gl_N.

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.