Notes on a homomorphism from the affine Yangian associated with $\hat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915267892740096 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | In the previous paper, we constructed a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the standard degreewise completion of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$. In this article, by using this homomorphism, we construct homomorphisms from the affine Yangian to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$, which are different from the one in \cite{U7}. Based on this result, we discuss a new definition of the affine shifted Yangian, from which it is expected that there exists a homomorphism to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$. In the appendix, we also show that this homomorphism is related to the one from the quantum affine algebra associated with $\widehat{\mathfrak{sl}}(n)$ to the quantum affine algebra associated with $\widehat{\mathfrak{sl}}(n+1)$ given by Li. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01870 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Notes on a homomorphism from the affine Yangian associated with $\hat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$ Ueda, Mamoru Quantum Algebra Rings and Algebras Representation Theory 17B37, 17B69 In the previous paper, we constructed a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the standard degreewise completion of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$. In this article, by using this homomorphism, we construct homomorphisms from the affine Yangian to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$, which are different from the one in \cite{U7}. Based on this result, we discuss a new definition of the affine shifted Yangian, from which it is expected that there exists a homomorphism to the universal enveloping algebra of a non-rectangular $W$-algebra of type $A$. In the appendix, we also show that this homomorphism is related to the one from the quantum affine algebra associated with $\widehat{\mathfrak{sl}}(n)$ to the quantum affine algebra associated with $\widehat{\mathfrak{sl}}(n+1)$ given by Li. |
| title | Notes on a homomorphism from the affine Yangian associated with $\hat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$ |
| topic | Quantum Algebra Rings and Algebras Representation Theory 17B37, 17B69 |
| url | https://arxiv.org/abs/2402.01870 |