Orthogonal Dualities of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister

Abstract

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 that the resulting duality functions between the dynamic stochastic higher spin vertex models and non-dynamic stochastic higher spin vertex models are the ${}_3 \varphi_2$ functions. A degeneration of these duality functions is dual $q$-Krawtchouk polynomials, which agree with the orthogonal polynomial dualities of Groenevelt--Wagenaar arXiv:2306.12318 between dynamic ASEP and ASEP. The method relies on the universal twister of $U_q(\mathfrak{sl}_2)$, regarded as a quasi-triangular quasi-Hopf algebra. Since the algebraic construction is formulated in a general setting, it is expected to produce duality functions for many other dynamic integrable models as well.