  We construct algebra homomorphisms from affine Yangians to the current
algebras of rectangular $W$-algebras both in type A. The construction is given
via the coproduct and the evaluation map for the affine Yangians. As a
consequence, we show that parabolic inductions for representations of the
rectangular $W$-algebras can be regarded as tensor product representations of
the affine Yangians under the homomorphisms. The same method is applicable also
to the super setting.
