Screening operators for W -algebras
Screening operators for W -algebras
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发表时间：
2017
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通讯作者：
Naoki Genra
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作者：
Naoki Genra
设g是具有非退化超对称偶不变双线性型的简单有限维李超代数，f是g的偶部分中的幂零元，（cid：2）是g对f的好分次，Wk（g，f ;（cid：2））是由广义Drinfeld-Sokolov约化定义的与g，f，k（cid：2）相关联的（afine）W -代数.在本文中，我们提出每个W -代数作为屏蔽算子的核的交集，作用在一个afine顶点超代数和一个中性自由超费米子顶点超代数的张量顶点超代数上。作为应用，我们证明了与osp（1，2 n）中的正则幂零元相关联的W -代数与Fateev和Lukyanov引入的W B n代数同构，与sl n中的次正则幂零元相关联的W -代数与Feigin和Semikhatov引入的W（2）n -代数同构.
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 , (cid:2) a good grading of g for f and W k ( g , f ; (cid:2)) the (affine) W -algebra associated with g , f , k , (cid:2) 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 , 2 n ) is isomorphic to the W B n algebra introduced by Fateev and Lukyanov, and that the W -algebra associated with a subregular nilpotent element in sl n is isomorphic to the W ( 2 ) n -algebra introduced by Feigin and Semikhatov.