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

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.

Keywords: Yangian, edge contraction, $W$-algebra, coset.

MSC: 17B37, 17B69

Received: August 8, 2025; in final form January 8, 2026; Published online January 31, 2026

Language: English

DOI: 10.3842/SIGMA.2026.007

ArXiv: 2407.15367