On W algebras commuting with a set of screenings
Alexey Litvinov, Lev Spodyneiko

TL;DR
This paper classifies W algebras that commute with specific exponential screening operators, focusing on those with a nontrivial spin 3 current, and derives equations governing these operators.
Contribution
It provides a classification of W algebras commuting with a set of screenings, including equations for screening operators with a spin 3 current.
Findings
Derived equations for screening operators
Classified solutions for W algebras with spin 3 currents
Extended understanding of W algebra structures
Abstract
We consider the problem of classification of all W algebras which commute with a set of exponential screening operators. Assuming that the W algebra has a nontrivial current of spin 3, we find equations satisfied by the screening operators and classify their solutions.
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