
TL;DR
This paper expresses W-algebras as intersections of kernels of screening operators on tensor vertex superalgebras, providing new isomorphisms with known W-algebras in specific cases.
Contribution
It introduces a novel description of W-algebras via screening operators, linking them to tensor vertex superalgebras and establishing isomorphisms with known algebraic structures.
Findings
W-algebras are realized as intersections of screening kernels.
Proved isomorphism between W-algebra for regular nilpotent in osp(1,2n) and W B_n.
Established isomorphism between W-algebra for subregular nilpotent in sl(n) and W^{(2)}_n.
Abstract
Let be a simple finite-dimensional Lie superalgebra with a non-degenerate supersymmetric even invariant bilinear form, a nilpotent element in the even part of , a good grading of for and the -algebra associated with defined by the generalized Drinfeld-Sokolov reduction. In this paper, we present each -algebra as the intersection of kernels of the screening operators, acting on the tensor vertex superalgebra of an affine vertex superalgebra and a neutral free superfermion vertex superalgebra. As applications, we prove that the -algebra associated with a regular nilpotent element in is isomorphic to the -algebra introduced by Fateev and Lukyanov, and that the -algebra…
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