  The q-oscillator representation for the Borel subalgebra of the affine
symmetry $U_q(sl_N^)$ is presented. By means of this q-oscillator
representation, we give the free field realizations of the Baxter's Q-operator
$Q_j(t)$, $\bar{Q}_j(t)$ for the W-algebra $W_N$. We give the functional
relations of the $T$-$Q$ operators, including the higher-rank generalization of
the Baxter's $T$-$Q$ relation.
