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, the authors 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