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.

35 pages

References in corpus (1)

• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities

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