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

Abstract

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

A mistake for the case n=3 is corrected

References in corpus (1)

• Regularity of fixed-point vertex operator subalgebras

Cited by in corpus (1)

• W-algebras as coset vertex algebras