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arXiv · 2407.15367

Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions

Mamoru Ueda
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Abstract

In the previous paper, we constructed two kinds of edge contractions for the affine super Yangian and a homomorphism from the affine super Yangian to the universal enveloping algebra of a $W$-superalgebra of type $A$. In this article, we show that these two edge contractions commute with each other. As an application, we give a homomorphism from the affine super Yangian to some centralizer algebras of the universal enveloping algebra of $W$-superalgebras of type $A$. Using the edge contraction, we also show the compatibility of the coproduct for the affine super Yangian with the parabolic induction for a $W$-superalgebra of type $A$ in some special cases.

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BibTeXRIS

Mamoru Ueda. 2024-07-22. Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions. https://doi.org/10.3842/sigma.2026.007

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