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Level-Rank Duality for Vertex Operator Algebras of types B and D
by Cuipo Jiang   Ching Hung Lam

Vol. 14 No. 1 (2019) P.31~P.54
 DOI: https://doi.org/10.21915/BIMAS.2019103 10.21915/BIMAS.2019103

ABSTRACT

For the simple Lie algebra $\frak{so}_m$, we study the commutant vertex operator algebra of $L_{\widehat{\frak{so}}_{m}}(n,0)$ in the $n$-fold tensor product $L_{\widehat{\frak{so}}_{m}}(1,0)^{\otimes n}$. It turns out that this commutant vertex operator algebra can be realized as a fixed point subalgebra of $L_{\widehat{\frak{so}}_{n}}(m,0)$ (or its simple current extension) associated with a certain abelian group. This result may be viewed as a version of level-rank duality.

KEYWORDS
level rank duality, vertex operator algebras, affine Lie algebras.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 17B69

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