Irreducible Wakimoto-like Modules for the Lie Superalgebra D(2, 1;.)

By using the idea of Wakimoto.s free field, we construct a class of representations for the Lie superalgebra D(2, 1; .) on the tensor product of a polynomial algebra and an exterior algebra involving one parameter .. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact, the representation is irreducible if and only if the parameter . satisfies (.+m)(..1+..m).0 for any m . .+.