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By the Baxter's $Q_{72}$-operator method, we demonstrate the equivalenttheory between the generalized $\tau^{(2)}$-model (other than two special caseswith a pseudovacuum state) and the $N$-state chiral Potts model with twoalternating vertical rapidities, where the degenerate models are included. As aconsequence, the theory of the XXZ chain model associated to cyclicrepresentations (with the parameter $\varsigma$) of $U_{\sf q}(sl_2)$ with${\sf q}^N=1$ for odd $N$ is identified with either (for $\varsigma^N=1$) thechiral Potts model with two superintegrable vertical rapidities, or (for$\varsigma^N \neq 1$) the degenerate model for the selfdual solution of thestar-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 thefunctional relations hold as in the solvable $N$-state chiral Potts model.

On the Equivalent Theory of the Generalized \tau^{(2)}-model and the Chiral Potts Model with two Alternating Vertical Rapidities