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arXiv · 2404.14096

The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras

Mamoru Ueda
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Abstract

By using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras, we construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$, which is an affine analogue of the one given in De Sole-Kac-Valeri. As a consequence, we find that the coproduct for the affine Yangian is compatible with some of the parabolic induction for non-rectangular $W$-algebras via this homomorphism. We also show that the image of this homomorphism is contained in the affine coset of the $W$-algebra in the special case that the $W$-algebra is associated with a nilpotent element of type $(1^{m-n},2^n)$.

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BibTeXRIS

Mamoru Ueda. 2024-04-22. The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras. https://arxiv.org/abs/2404.14096

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