Rationality of W-algebras: principal nilpotent cases
Rationality of W-algebras: principal nilpotent cases
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DOI：
10.4007/annals.2015.182.2.4
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发表时间：
2015-09-01
影响因子：
4.9
通讯作者：
Arakawa, Tomoyuki
中科院分区：
文献类型：
--
作者：
Arakawa, Tomoyuki
本文证明了Frenkel，Kac和Wakimoto所发现的所有极小级数主W-代数的合理性，从而给出了一类新的有理C-2-余有限顶点算子代数.在我们的证明中的一个关键成分是通过量子化Drinfeld-Sokolov约化来研究单W-代数的朱代数。证明了取朱代数的函子与约化函子可交换。利用这一一般性事实，我们还确定了与仿射Kac-Moody代数的容许表示相关联的顶点算子代数的朱氏代数的关联分次的极大谱。
We prove the rationality of all the minimal series principal W-algebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C-2-cofinite vertex operator algebras. A key ingredient in our proof is the study of Zhu's algebra of simple W-algebras via the quantized Drinfeld-Sokolov reduction. We show that the functor of taking Zhu's algebra commutes with the reduction functor. Using this general fact we determine the maximal spectrums of the associated graded of Zhu's algebras of vertex operator algebras associated with admissible representations of affine Kac-Moody algebras as well.