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In [1], the spectrum (eigenvalues and eigenstates) of a latticeregularizations of the Sine-Gordon model has been completely characterized interms of polynomial solutions with certain properties of the Baxter equation.This characterization for cyclic representations has been derived by the use ofthe Separation of Variables (SOV) method of Sklyanin and by the directconstruction of the Baxter Q-operator family. Here, we reconstruct the BaxterQ-operator and the same characterization of the spectrum by only using the SOVmethod. This analysis allows us to deduce the main features required for theextension to cyclic representations of other integrable quantum models of thiskind of spectrum characterization.

Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models