Suggestion of a definition of the twisted affine Yangian of type $D$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908746215587840 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | We suggest a definition of the 1-parameter twisted affine Yangian $TY_{\hbar}(\widehat{\mathfrak{so}}(n))$ and the 2-parameter twisted affine Yangian $TY_{\hbar,\ve}(\widehat{\mathfrak{so}}(2n))$. These twisted affine Yangians are deformations of subalgebras of the universal central extension of $\mathfrak{sl}(2n)[u^{\pm1},v]$. As for the 1-parameter twisted affine Yangian, we show that $TY_{\hbar}(\widehat{\mathfrak{so}}(n))$ is a coideal of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$. As for the two parameter twisted affine Yangian, we construct a homomorphism from $TY_{\hbar,\ve}(\widehat{\mathfrak{so}}(8))$ to the universal enveloping algebra of the rectangular $W$-algebra $\mathcal{W}^k(\mathfrak{sp}(16),(2^8))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Suggestion of a definition of the twisted affine Yangian of type $D$ Ueda, Mamoru Rings and Algebras 17B37, 17B69 We suggest a definition of the 1-parameter twisted affine Yangian $TY_{\hbar}(\widehat{\mathfrak{so}}(n))$ and the 2-parameter twisted affine Yangian $TY_{\hbar,\ve}(\widehat{\mathfrak{so}}(2n))$. These twisted affine Yangians are deformations of subalgebras of the universal central extension of $\mathfrak{sl}(2n)[u^{\pm1},v]$. As for the 1-parameter twisted affine Yangian, we show that $TY_{\hbar}(\widehat{\mathfrak{so}}(n))$ is a coideal of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$. As for the two parameter twisted affine Yangian, we construct a homomorphism from $TY_{\hbar,\ve}(\widehat{\mathfrak{so}}(8))$ to the universal enveloping algebra of the rectangular $W$-algebra $\mathcal{W}^k(\mathfrak{sp}(16),(2^8))$. |
| title | Suggestion of a definition of the twisted affine Yangian of type $D$ |
| topic | Rings and Algebras 17B37, 17B69 |
| url | https://arxiv.org/abs/2512.06340 |