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

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.

16 pages, minor changes

References in corpus (2)

• Elementary invariants for centralizers of nilpotent matrices
• Classical $\mathcal{W}$-algebras for centralizers

Cited by in corpus (1)

• Generalized finite and affine $W$-algebras in type $A$