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$W$-algebras associated with centralizers in type $A$ (2002.02218v2)
Published 6 Feb 2020 in math.RT, math-ph, and math.MP
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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