
Rationality of Walgebras: principal nilpotent casesRationality of Walgebras: principal nilpotent casesAA00532843 
"/Arakawa, Tomoyuki/"Arakawa, Tomoyuki
182
(
2
)
, pp.565

604 , 20150730 , Department of Mathematics of Princeton University
ISSN:0003486X
NCID:AA00532843
Description
We prove the rationality of all the minimal series principal Walgebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C2cofinite vertex operator algebras. A key ingredient in our proof is the study of Zhu’s algebra of simple Walgebras via the quantized DrinfeldSokolov 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 KacMoody algebras as well.
FullText
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