  By the Baxter's $Q_{72}$-operator method, we demonstrate the equivalent
theory between the generalized $\tau^{(2)}$-model (other than two special cases
with a pseudovacuum state) and the $N$-state chiral Potts model with two
alternating vertical rapidities, where the degenerate models are included. As a
consequence, the theory of the XXZ chain model associated to cyclic
representations (with the parameter $\varsigma$) of $U_{\sf q}(sl_2)$ with
${\sf q}^N=1$ for odd $N$ is identified with either (for $\varsigma^N=1$) the
chiral Potts model with two superintegrable vertical rapidities, or (for
$\varsigma^N \neq 1$) the degenerate model for the selfdual solution of the
star-triangle relation. In all these identifications, the transfer matrices $T,
\hat{T}$ of the chiral Potts model (including the degenerate ones) serve as the
$Q_R, Q_L$-operators of the corresponding $\tau^{(2)}$-model, so that the
functional relations hold as in the solvable $N$-state chiral Potts model.
