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arXiv · 2002.02218

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

A. I. Molev
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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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BibTeXRIS

A. I. Molev. 2020-02-06. $W$-algebras associated with centralizers in type $A$. https://doi.org/10.1093/imrn%2Frnaa271

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