  We study a two-component asymmetric simple exclusion process (ASEP) that is
equivalent to the ASEP with second-class particles. We prove self-duality with
respect to a family of duality functions which are shown to arise from the
reversible measures of the process and the symmetry of the generator under the
quantum algebra $U_q[\mathfrak{gl}_3]$. We construct all invariant measures in
explicit form and discuss some of their properties. We also prove a sum rule
for the duality functions.
