SIGMA 22 (2026), 007, 37 pages      arXiv:2407.15367      https://doi.org/10.3842/SIGMA.2026.007

Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions

Mamoru Ueda
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan

Received August 08, 2025, in final form January 08, 2026; Published online January 31, 2026

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.

Key words: Yangian; edge contraction; $W$-algebra; coset.

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