Coproduct for affine Yangians and parabolic induction for rectangular W-algebras

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.

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