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We construct explicitly a large family of Gelfand-Tsetlin modules for anarbitrary finite W-algebra of type A and establish their irreducibility. Abasis of these modules is formed by the Gelfand-Tsetlin tableaux whose entriessatisfy certain admissible sets of relations. Characterization and an effectivemethod of constructing such admissible relations are given. In the case of theYangian of gl_n we prove the sufficient condition for the irreducibility of thetensor product of two highest weight relation modules and establishirreducibility of any number of highest weight relation modules with generichighest weights. This extends the results of Molev to infinite dimensionalhighest modules.

Relation modules for finite W-algebras and tensor products of highest weight evaluation modules for Yangians of type A