Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two

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We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. As an application, an expression for the r-th moment of the exponentiated current is written in terms of r-particle evolution. The construction and proofs of duality are accomplished using symmetry of the quantum groups Uq(gl₃) and Uq(sp₄), with each node in the Dynkin diagram corresponding to a particle type, and the number of edges corresponding to the jump rates.