Parabolic presentations of Yangian in types $B$ and $C$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913725045276672 |
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| author | Chang, Zhihua Jing, Naihuan Liu, Ming Ma, Haitao |
| author_facet | Chang, Zhihua Jing, Naihuan Liu, Ming Ma, Haitao |
| contents | We establish a parabolic presentation of the extended Yangian $\X(\mathfrak{g}_{N})$ associated with the Lie algebras $\mathfrak{g}_{N}$ of type $B$ and $C$, parameterized by a symmetric composition $ν$ of $N$. By formulating a block matrix version of the RTT presentation of $\X(\mathfrak{g}_{N})$, we systematically derive the generators and relations through the Gauss decomposition of the generator matrix in $ν$-block form. Furthermore, leveraging this parabolic presentation, we obtain a novel formula for the center of $\X(\mathfrak{g}_{N})$, offering new insights into its structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic presentations of Yangian in types $B$ and $C$ Chang, Zhihua Jing, Naihuan Liu, Ming Ma, Haitao Representation Theory Quantum Algebra Primary: 17B37, secondary: 81R51 We establish a parabolic presentation of the extended Yangian $\X(\mathfrak{g}_{N})$ associated with the Lie algebras $\mathfrak{g}_{N}$ of type $B$ and $C$, parameterized by a symmetric composition $ν$ of $N$. By formulating a block matrix version of the RTT presentation of $\X(\mathfrak{g}_{N})$, we systematically derive the generators and relations through the Gauss decomposition of the generator matrix in $ν$-block form. Furthermore, leveraging this parabolic presentation, we obtain a novel formula for the center of $\X(\mathfrak{g}_{N})$, offering new insights into its structure. |
| title | Parabolic presentations of Yangian in types $B$ and $C$ |
| topic | Representation Theory Quantum Algebra Primary: 17B37, secondary: 81R51 |
| url | https://arxiv.org/abs/2502.21211 |