Higher spin representations of the Yangian of $\mathfrak{sl}_2$ and R-matrices
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918267444002816 |
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| author | Yang, Yaping Zinn-Justin, Paul |
| author_facet | Yang, Yaping Zinn-Justin, Paul |
| contents | We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin [BZJ20]. When the framing dimension is 1, it recovers the evaluation pullback of the $\ell+1$-dimensional irreducible representation of $\mathfrak{sl}_2$. We introduce the lattice model and prove that its partition function coincides with the weight function constructed using the framed shuffle formula. The latter follows the approach of Rimányi, Tarasov and Varchenko [RTV15]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher spin representations of the Yangian of $\mathfrak{sl}_2$ and R-matrices Yang, Yaping Zinn-Justin, Paul Representation Theory Mathematical Physics Algebraic Geometry Primary 17B37, Secondary 55N22, 16G20 We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin [BZJ20]. When the framing dimension is 1, it recovers the evaluation pullback of the $\ell+1$-dimensional irreducible representation of $\mathfrak{sl}_2$. We introduce the lattice model and prove that its partition function coincides with the weight function constructed using the framed shuffle formula. The latter follows the approach of Rimányi, Tarasov and Varchenko [RTV15]. |
| title | Higher spin representations of the Yangian of $\mathfrak{sl}_2$ and R-matrices |
| topic | Representation Theory Mathematical Physics Algebraic Geometry Primary 17B37, Secondary 55N22, 16G20 |
| url | https://arxiv.org/abs/2403.17433 |