𝒲-Algebras Associated With Centralizers in Type A

DOI10.1093/IMRN/RNAA271zbMATH Open1494.81009arXiv2002.02218OpenAlexW3097244851MaRDI QIDQ5071151

Alexander I. Molev

Publication date: 20 April 2022

Published in: Unnamed Author (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2002.02218

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15)

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