Coset vertex operator algebras and W-algebras of A-type

We give an explicit description for a weight three generator of the coset vertex operator algebra , for n ae<yen> 2, l > 1. Furthermore, we prove that the commutant is isomorphic to the W-algebra , which confirms the conjecture for the sl3 case that is isomorphic to for simply-laced Lie algebras g with its Coxeter number h for a positive integer l.