  We construct representations $\hat\pi_{\br}$ of the quantum algebra
$U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of
formal power series of $n(n-1)/2$ non-commuting variables. These variables
generate a flag manifold of the matrix quantum group $SL_q(n)$ which is dual to
$U_q(sl(n))$. The conditions for reducibility of $\hat\pi_{\br}$ and the
procedure for the construction of the $q$ - difference intertwining operators
are given. The representations and $q$ - difference intertwining operators are
given in the most explicit form for $n=3$. In the Note Added some general
results for arbitrary $n$ are given.
