A level-rank duality for parafermion vertex operator algebras of type A
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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 $W_{sl_{k}}(1,1)\otimes W_{sl_{k}}(1,2) \otimes \cdots \otimes W_{sl_{k}}(1,n-1)$.References
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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
- MR Author ID: 363106
- Email: chlam@math.sinica.edu.tw
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 4133-4142
- MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/S0002-9939-2014-12167-8
- MathSciNet review: 3266984