  We present an explicit representation for the matrix product ansatz for some
two-species TASEP with open boundary conditions. The construction relies on the
integrability of the models, a property that constrains the possible rates at
the boundaries. The realisation is built on a tensor product of copies of the
DEHP algebras. Using this explicit construction, we are able to calculate the
partition function of the models. The densities and currents in the stationary
state are also computed. It leads to the phase diagram of the models. Depending
on the values of the boundary rates, we obtain for each species shock waves,
maximal current, or low/high densities phases.
