Resumen de Screening operators for W-algebras

Naoki Genra

• Let g be a simple finite-dimensional Lie superalgebra with a non-degenerate supersymmetric even invariant bilinear form, f a nilpotent element in the even part of g, a good grading of g for f and Wk (g, f ; ) the (affine) W-algebra associated with g, f, k, defined by the generalized Drinfeld–Sokolov reduction. In this paper, we present each W-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 W-algebra associated with a regular nilpotent element in osp(1, 2n) is isomorphic to the WBnalgebra introduced by Fateev and Lukyanov, and that the W-algebra associated with a subregular nilpotent element in sln is isomorphic to the W(2) n -algebra introduced by Feigin and Semikhatov.