Selecta Mathematica· 2026Q1
The coproduct for the affine Yangian and the parabolic induction for non-rectangular W-algebras
- 3citations
- Q1SCImago
- 2026year
Short summary
A homomorphism is constructed from the affine Yangian of $\widehat{\mathfrak {sl}}(n)$ to the universal enveloping algebra of a non-rectangular W-algebra of type A, establishing compatibility between the affine Yangian coproduct and parabolic induction for these W-algebras.
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Key points
- A homomorphism is established from the affine Yangian of $\widehat{\mathfrak {sl}}(n)$ to the universal enveloping algebra of a non-rectangular W-algebra of type A.
- The homomorphism is an affine analogue of the one presented by De Sole-Kac-Valeri [6].
- The coproduct of the affine Yangian is shown to be compatible with parabolic induction for non-rectangular W-algebras via this homomorphism.
- This work is expected to contribute to the resolution of the Crutzig-Diaconescu-Ma conjecture.
AI-generated from the title and abstract; the full text is not read.
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 [6]. As a consequence, we find that the coproduct for the affine Yangian is compatible with the parabolic induction for non-rectangular W-algebras via this homomorphism. It is expected that this homomorphism will be helpful for the resolution of the Crutzig-Diaconescu-Ma’s conjecture.
The authors' abstract, as published at the source. Selecta Mathematica, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics