Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908814625734656 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions Ueda, Mamoru Rings and Algebras Mathematical Physics Quantum Algebra 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. |
| title | Commuting Subalgebras of Affine Super Yangians Arising from Edge Contractions |
| topic | Rings and Algebras Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2407.15367 |