  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 $U_q(\mathfrak{gl}_3)$ and $U_q(\mathfrak{sp}_4)$, with each
node in the Dynkin diagram corresponding to a particle type, and the number of
edges corresponding to the jump rates.
