  This paper is a continuation of our papers \cite{EK1, EK2}. In \cite{EK2} we
showed that for the root system $A_{n-1}$ one can obtain Macdonald's
polynomials as weighted traces of intertwining operators between certain
finite-dimensional representations of $U_q(sl_n)$. The main goal of the present
paper is to use this construction to give a representation-theoretic proof of
Macdonald's inner product and symmetry identities for the root system
$A_{n-1}$. The proofs are based on the techniques of ribbon graphs developed by
Reshetikhin and Turaev. We also use the symmetry identities to derive recursive
relations for Macdonald's polynomials.
