Level-Rank Duality for Vertex Operator Algebras of types B and D

Abstract: For the simple Lie algebra $ \frak{so}m$, we study the commutant vertex operator algebra of $ L{\hat{\frak{so}}{m}}(n,0)$ in the $n$-fold tensor product $ L{\hat{\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 $L{\hat{\frak{so}}_{n}}(m,0)$ (or its simple current extension) associated with a certain abelian group. This result may be viewed as a version of level-rank duality.