Stochastic Baxterisation of a fused Hecke algebra

Abstract: Baxterisation is a procedure which constructs solutions of the Yang-Baxter equation from algebra representations. A paper arXiv:2004.05035 provides Baxterisation formulas for a fused Hecke algebra. In this paper, we provide a stochastic version of Baxterisation for the fused Hecke algebra, which yields stochastic solutions to the Yang-Baxter equation. The coefficients in the Baxterisation formula previously appeared as the $q$-Hahn weights. This results in new formulas for the weights of the stochastic higher-spin vertex model.