  This paper introduces a multi-species version of a process called ASEP(q,j).
In this process, up to 2j particles are allowed to occupy a lattice site, the
particles drift to the right with asymmetry 0<q^{2j}<1, and there are n-1
species of particles in which heavier particles can force lighter particles to
switch places. Assuming closed boundary conditions, we explicitly write the
reversible measures and a self-duality function, generalizing previously known
results for two-species ASEP and single-species ASEP(q,j).
  Additionally, it is shown that this multi-species ASEP(q,j) is dual to its
space-reversed version, in which particles drift to the left. As j goes to
infinity, this multi-species ASEP(q,j) converges to a multi-species q-TAZRP and
the self-duality function has a non-trivial limit, showing that this
multi-species q-TAZRP satisfies a space-reversed self-duality.
  The construction of the process and the proofs are accomplished utilizing
spin j representations of U_q(gl_n), extending the approach used for
single-species ASEP(q,j).
