  We study an inhomogenous multispecies version of the Totally Asymmetric
Simple Exclusion Process (TASEP) on a periodic oriented one dimensional
lattice, which depends on two sets of parameters $({\bf \tau},{\bf \nu})$,
attached to the particles. After discussing the Yang-Baxter integrability of
our model, we study its (unnormalized) stationary measure. Motivated by the
integrability of the model we introduce a further set of spectral parameters
${\bf z}$, attached to the sites of the lattice, and we uncover a remarkable
underlying algebraic structure. We provide exact formulas for the stationary
measure and prove the factorization of the stationary probability of certain
configurations in terms of double Schubert polynomials in $({\bf \tau},{\bf
\nu})$.
