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

Abstract

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.

arXiv comment35 pages

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Cited by in corpus (4)

• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• On the structure of W-algebras in type A
• An Overview of Crystals and Double Quiver Yangians