**Separation of variables in the Baxter-Bazhanov-Stroganov model**

**Abstract:**

The Baxter-Bazhanov-Stroganov model (also known as the t^{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}(l) 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 t^{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. These solutions give explicit
formulas for eigenvectors of Ising transfer-matrix. Using them, we proved formula for form-factors in the Ising model on
finite lattice.

Joint work with *G. von Gehlen, S. Pakuliak, V. Shadura, Yu. Tykhyy*.