  We consider the integrable spin chain model - the noncompact SL(2,R) spin
magnet. The spin operators are realized as the generators of the unitary
principal series representation of the SL(2,R) group. In an explicit form, we
construct R-matrix, the Baxter Q-operator and the transition kernel to the
representation of the Separated Variables (SoV). The expressions for the energy
and quasimomentum of the eigenstates in terms of the Baxter Q-operator are
derived. The analytic properties of the eigenvalues of the Baxter operator as a
function of the spectral parameter are established. Applying the diagrammatic
approach, we calculate Sklyanin's integration measure in the separated
variables and obtain the solution to the spectral problem for the model in
terms of the eigenvalues of the Q-operator. We show that the transition kernel
to the SoV representation is factorized into a product of certain operators
each depending on a single separated variable.
