Stochastic Baxterisation of a fused Hecke algebra

TL;DR

This paper introduces a stochastic Baxterisation method for the fused Hecke algebra, producing stochastic solutions to the Yang-Baxter equation and new weights for the stochastic higher-spin vertex model.

Contribution

It extends the Baxterisation of the fused Hecke algebra to a stochastic setting, linking algebraic formulas to probabilistic models.

Findings

Derived stochastic solutions to the Yang-Baxter equation.

Provided new weight formulas for the stochastic higher-spin vertex model.

Connected algebraic Baxterisation with probabilistic weights.

Abstract

Baxterisation is a procedure which constructs solutions of the Yang-Baxter equation from algebra representations. A recent 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.