Orthogonal Dualities and Asymptotics of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916250202931200 |
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| author | Kuan, Jeffrey Zhou, Zhengye |
| author_facet | Kuan, Jeffrey Zhou, Zhengye |
| contents | We introduce a new, algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, where we prove the duality functions are the $ _3 φ_2$ functions. A degeneration of these duality functions are orthogonal polynomial dualities of Groenevelt--Wagener arXiv:2306.12318. The method involves using the universal twister of $\mathcal{U}_q(\mathfrak{sl}_2)$, viewed as a quasi--triangular, quasi--$^*$--Hopf algebra. The algebraic method is presented very generally and is expected to produce duality functions for other dynamic integrable models. As an application of the duality, we prove that the asymptotic fluctuations of the dynamic stochastic six vertex model with step initial conditions are governed by the Tracy--Widom distribution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_17602 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orthogonal Dualities and Asymptotics of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister Kuan, Jeffrey Zhou, Zhengye Probability Mathematical Physics Quantum Algebra We introduce a new, algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, where we prove the duality functions are the $ _3 φ_2$ functions. A degeneration of these duality functions are orthogonal polynomial dualities of Groenevelt--Wagener arXiv:2306.12318. The method involves using the universal twister of $\mathcal{U}_q(\mathfrak{sl}_2)$, viewed as a quasi--triangular, quasi--$^*$--Hopf algebra. The algebraic method is presented very generally and is expected to produce duality functions for other dynamic integrable models. As an application of the duality, we prove that the asymptotic fluctuations of the dynamic stochastic six vertex model with step initial conditions are governed by the Tracy--Widom distribution. |
| title | Orthogonal Dualities and Asymptotics of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister |
| topic | Probability Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2305.17602 |