  The algebra of monodromy matrices for sl(n) trigonometric R-matrices is
studied. It is shown that a generic finite-dimensional polynomial irreducible
representation of this algebra is equivalent to a tensor product of
L-operators. Cocommutativity of representations is discussed. A special class
of representations - factorizable representations is introduced and
intertwiners for cocommuting factorizable representations are written through
the Boltzmann weights of the sl(n) chiral Potts model.
  Let us consider an algebra generated by noncommutative entries of the matrix
$T(u)$ satisfying the famous bilinear relation originated from the quantum
inverse scattering method: $R(\la-\mu)T(\la)T(\mu)=T(\mu)T(\la) R(\la-\mu)$
where $R(\la)$ is R-matrix. For historical reasons this algebra is called the
algebra of monodromy matrices. If $\g$ is a simple finite-dimensional Lie
algebra and $R(\la)$ is $\g$-invariant R-matrix the algebra of monodromy
matrices after a proper specialization gives the Yangian $Y(\g)$ introduced by
Drinfeld. If $R(\la)$ is corresponding trigonometric R-matrix this algebra is
closely connected with $U_q(\g)$ and $U_q(\hat\g)$ at zero level. If $R(\la)$
is $sl(2)$ elliptic R-matrix the algebra of monodromy matrices gives rise to
Sklyanin's algebra.
  In this paper we shall study algebras of monodromy matrices for $sl(n)$
trigonometric R-matrices at roots of 1. Finite-dimensional cyclic irreducible
polynomial representations and their intertwiners are discussed.
