The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911086199963648 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | 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 $(1^{m-n},2^n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras Ueda, Mamoru Rings and Algebras Mathematical Physics Quantum Algebra 17B37, 17B69 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 $(1^{m-n},2^n)$. |
| title | The coproduct for the affine Yangian and the parabolic induction for non-rectangular $W$-algebras |
| topic | Rings and Algebras Mathematical Physics Quantum Algebra 17B37, 17B69 |
| url | https://arxiv.org/abs/2404.14096 |