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

We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles, which will be called type A2 ASEP and type C2 ASEP. Particles of type 1 force particles of type 2 to switch places. In the C2 case, particles of type 2 can only influence the jump rates of particles of type 1, and in the A2 case particles of type 2 do not influence particles of type 1 at all. We prove that the processes are self-dual and explicitly write the duality function, which is a generalization of the self-duality function for ASEP. The construction and proofs of duality are accomplished using symmetry of the quantum groups and for the A2 and C2 ASEP respectively.