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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 offormal power series of $n(n-1)/2$ non-commuting variables. These variablesgenerate 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 theprocedure for the construction of the $q$ - difference intertwining operatorsare given. The representations and $q$ - difference intertwining operators aregiven in the most explicit form for $n=3$. In the Note Added some generalresults for arbitrary $n$ are given.Comment: 24 pages; v2 includes Note Added published in J.Phys. A27 (1994),  references update

q-difference intertwining operators for Uq(sl(n)): general setting and the case n=3

q-difference intertwining operators for U_q(sl(n)): general setting and the case n=3