The commutant of Lslˆ2(n,0) in the vertex operator algebra Lslˆ2(1,0)⊗n

We study the commutant Lslˆ2(n,0)c of Lslˆ2(n,0) in the vertex operator algebra Lslˆ2(1,0)⊗n, for n≥2n≥2. The main results include a complete classification of all irreducible Lslˆ2(n,0)c-modules and that Lslˆ2(n,0)c is a rational vertex operator algebra. As a consequence, every irreducible Lslˆ2(n,0)c-module arises from the coset construction as conjectured in [37].