Triangular solutions to the reflection equation for $U_q(\widehat{sl_n})$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916289329496064 |
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| author | Kolyaskin, Dmitry Mangazeev, Vladimir V |
| author_facet | Kolyaskin, Dmitry Mangazeev, Vladimir V |
| contents | We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct upper- and lower-triangular solutions of the reflection equation related to symmetric tensor representations of $U_q(\widehat{sl_n})$ with arbitrary spin. We also prove the star-star relation for the Boltzmann weights of the Ising-type model, conjectured by Bazhanov and Sergeev, and use it to verify certain properties of the solutions obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_05442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triangular solutions to the reflection equation for $U_q(\widehat{sl_n})$ Kolyaskin, Dmitry Mangazeev, Vladimir V Mathematical Physics Statistical Mechanics Quantum Algebra We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct upper- and lower-triangular solutions of the reflection equation related to symmetric tensor representations of $U_q(\widehat{sl_n})$ with arbitrary spin. We also prove the star-star relation for the Boltzmann weights of the Ising-type model, conjectured by Bazhanov and Sergeev, and use it to verify certain properties of the solutions obtained. |
| title | Triangular solutions to the reflection equation for $U_q(\widehat{sl_n})$ |
| topic | Mathematical Physics Statistical Mechanics Quantum Algebra |
| url | https://arxiv.org/abs/2402.05442 |