Matrix product solution to multi-species ASEP with open boundaries

We study a class of multi-species ASEP with open boundaries. The boundaries are chosen in such a way that all species of particles interact non-trivially with the boundaries and are present in the stationary state. We give the exact expression of the stationary state in a matrix product form and we compute its normalisation. Densities and currents for the different species are then computed in term of this normalisation.