  We consider the totally asymmetric simple exclusion process (TASEP) on a
finite lattice with open boundaries. We show, using the recursive structure of
the Markov matrix that encodes the dynamics, that there exist two transfer
matrices $T_{L-1,L}$ and $\tilde{T}_{L-1,L}$ that intertwine the Markov
matrices of consecutive system sizes:
$\tilde{T}_{L-1,L}M_{L-1}=M_{L}T_{L-1,L}$. This semi-conjugation property of
the dynamics provides an algebraic counterpart for the matrix-product
representation of the steady state of the process.
