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A level-rank duality for parafermion vertex operator algebras of type A


Author: Ching Hung Lam
Journal: Proc. Amer. Math. Soc. 142 (2014), 4133-4142
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/S0002-9939-2014-12167-8
Published electronically: August 14, 2014
MathSciNet review: 3266984
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Abstract: We show that the tensor product of the parafermion vertex operator algebras $ K(sl_{k+1},n+1) \otimes K(sl_{n+1}, k+1)$ can be embedded as a full subVOA into the lattice VOA $ V_{A_n\otimes A_k}$. The decomposition of $ V_{A_n\otimes A_k}$ as a direct sum of irreducible $ K(sl_{k+1},n+1) \otimes K(sl_{n+1}, k+1)$-modules is also obtained. In addition, we show that the parafermion VOA $ K(sl_{n}, k)$ contains a full subVOA isomorphic to a tensor product of $ W$-algebras $ W_{sl_{k}}(1,1)\otimes W_{sl_{k}}(1,2) \otimes \cdots \otimes W_{sl_{k}}(1,n-1)$.


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Additional Information

Ching Hung Lam
Affiliation: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 10617 – and – National Center for Theoretical Sciences, Taiwan
Email: chlam@math.sinica.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-2014-12167-8
Received by editor(s): October 3, 2012
Received by editor(s) in revised form: February 6, 2013
Published electronically: August 14, 2014
Additional Notes: This work was partially supported by NSC grant 100-2628-M-001005-MY4, Taiwan
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.