Transfer matrix functional relations for the generalized τ ₂ (t _q) model

The N-state chiral Potts model in lattice statistical mechanics can be obtained as a "descendant" of the six-vertex model, via an intermediate "Q" or "τ ₂ (t _q)" model. Here we generalize this to obtain a column-inhomogeneous τ ₂ (t _q) model, and derive the functional relations satisfied by its row-to-row transfer matrix. We do not need the usual chiral Potts relations between the Nth powers of the rapidity parameters a _p, b _p, c _p, d _p of each column. This enables us to readily consider the case of fixed-spin boundary conditions on the left and right-most columns. We thereby re-derive the simple direct product structure of the transfer matrix eigenvalues of this model, which is closely related to the superintegrable chiral Potts model with fixed-spin boundary conditions.