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We study two generalizations of the asymmetric simple exclusion process withtwo 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 oftype 1. We prove that the processes are self-dual and explicitly write theduality function. As an application, an expression for the r-th moment of theexponentiated current is written in terms of r-particle evolution.  The construction and proofs of duality are accomplished using symmetry of thequantum groups $U_q(\mathfrak{gl}_3)$ and $U_q(\mathfrak{sp}_4)$, with eachnode in the Dynkin diagram corresponding to a particle type, and the number ofedges corresponding to the jump rates.

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