For W(2,2), tensor products of non-weight modules Omega(lambda,alpha,h) with a simple restricted module are simple exactly when the lambda parameters are pairwise distinct, and isomorphism classes are classified by the same data.
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New simple modules for the $W$-algebra $W(2,2)$
For W(2,2), tensor products of non-weight modules Omega(lambda,alpha,h) with a simple restricted module are simple exactly when the lambda parameters are pairwise distinct, and isomorphism classes are classified by the same data.