$RLL$-realization of two-parameter quantum affine algebra in type $D_n^{(1)}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910519422615552 |
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| author | Zhuang, Rushu Hu, Naihong Xu, Xiao |
| author_facet | Zhuang, Rushu Hu, Naihong Xu, Xiao |
| contents | We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. Using the Gauss decomposition of the $R$-matrix realization of $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$, we study the commutation relations of the Gaussian generators and finally arrive at its $RLL$-formalism of the Drinfeld realization of two-parameter quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $RLL$-realization of two-parameter quantum affine algebra in type $D_n^{(1)}$ Zhuang, Rushu Hu, Naihong Xu, Xiao Quantum Algebra primary 16T25, 17B37, 81R50, secondary 17B67 We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. Using the Gauss decomposition of the $R$-matrix realization of $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$, we study the commutation relations of the Gaussian generators and finally arrive at its $RLL$-formalism of the Drinfeld realization of two-parameter quantum affine algebra $U=U_{r,s}\mathcal(\widehat{\mathfrak{so}_{2n}})$. |
| title | $RLL$-realization of two-parameter quantum affine algebra in type $D_n^{(1)}$ |
| topic | Quantum Algebra primary 16T25, 17B37, 81R50, secondary 17B67 |
| url | https://arxiv.org/abs/2405.06581 |