A Short Note on Markov Duality in Multi-species Higher Spin Stochastic Vertex Models

Abstract

We show that the multi-species higher spin stochastic vertex model, also called the U_q(A_n^{(1)}) vertex model, satisfies a duality where the indicator function has the form {η^x_{[1,n]} \geq ξ^x_{[1,n]} }. In other words, for every particle in the ξconfiguration of species i at vertex x, there must be a particle of species j > i at vertex x in the ηconfiguration. The proof follows by applying charge reversal to previously discovered duality functions, which also results in open boundary conditions. As a corollary, we recover the duality for the stochastic six vertex model recently found by Y. Lin.

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