On the Connections of W Algebras from Different Reductions of WZNW Theory

The possible isomorphic relations between W algebras from various conformal reductions of WZNW model are investigated and the criterion for the isomorphism of W algebras is given.In the special case of sl₃ WZNW theory,we show explicitly the isomorphism between W(111)₂] and W(12)₁] and discuss the constraint-gauge condition transmutation between the O'Raifeartaigh gauges and the transmutation of conformal weights under the isomorphism transformation.