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 TL−1,L and T~L−1,L that intertwine the Markov
matrices of consecutive system sizes:
T~L−1,LML−1=MLTL−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.Comment: 7 page