Baxter-Bazhanov-Stroganov model: Separation of Variables and Baxter Equation

The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B_n(\lambda) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer matrices of the \tau^(2) model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.