Self-duality and shock dynamics in the n-species priority ASEP

We construct all invariant measures of the n-species priority asymmetric simple exclusion process with reflecting boundaries and prove reversibility. Using the symmetry of the generator of the process under the quantum algebra Uq[gl(n+1)] we derive self-duality functions. From these we obtain in explicit form the time evolution on Z of a family of measures with K shocks in terms of the transition probability of a shock exclusion process with K coloured particles with particle-dependent hopping rates and nearest-neighbour colour exchange. This process is a gas of particles that form a bound state, corresponding to shock coalescence on macroscopic scale.