Current browse context:
math.RA
Change to browse by:
References & Citations
Mathematics > Rings and Algebras
Title: The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras
(Submitted on 22 Apr 2024 (v1), last revised 27 Apr 2024 (this version, v3))
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 $(1^{m-n},2^n)$.
Submission history
From: Mamoru Ueda [view email][v1] Mon, 22 Apr 2024 11:31:26 GMT (12kb)
[v2] Tue, 23 Apr 2024 16:34:19 GMT (13kb)
[v3] Sat, 27 Apr 2024 20:39:47 GMT (13kb)
Link back to: arXiv, form interface, contact.