Two Homomorphisms from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910655254102016 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | We construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+\hbar}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$ which is different from the one in arXiv:2312.09933. By using this homomorphism, we give a homomorphism from $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))\otimes Y_{\hbar,\varepsilon+n\hbar}(\widehat{\mathfrak{sl}}(m))$ to $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(m+n))$. As an application, we construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+n\hbar}(\widehat{\mathfrak{sl}}(m))$ to the centralizer algebra of the pair of affine Lie algebras $(\widehat{\mathfrak{gl}}(m+n),\widehat{\mathfrak{gl}}(n))$ and the coset vertex algebra of the pair of rectangular $W$-algebras $(\mathcal{W}^k(\mathfrak{gl}(2m+2n),(2^{m+n})),\mathcal{W}^{k+m}(\mathfrak{sl}(2n),(2^{n})))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Homomorphisms from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$ Ueda, Mamoru Rings and Algebras Quantum Algebra 17B37, 17B69 We construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+\hbar}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$ which is different from the one in arXiv:2312.09933. By using this homomorphism, we give a homomorphism from $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))\otimes Y_{\hbar,\varepsilon+n\hbar}(\widehat{\mathfrak{sl}}(m))$ to $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(m+n))$. As an application, we construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+n\hbar}(\widehat{\mathfrak{sl}}(m))$ to the centralizer algebra of the pair of affine Lie algebras $(\widehat{\mathfrak{gl}}(m+n),\widehat{\mathfrak{gl}}(n))$ and the coset vertex algebra of the pair of rectangular $W$-algebras $(\mathcal{W}^k(\mathfrak{gl}(2m+2n),(2^{m+n})),\mathcal{W}^{k+m}(\mathfrak{sl}(2n),(2^{n})))$. |
| title | Two Homomorphisms from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$ |
| topic | Rings and Algebras Quantum Algebra 17B37, 17B69 |
| url | https://arxiv.org/abs/2404.10923 |