Baxter Q- operator and functional relations

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from the explicit calculations. We derive the Baxter equation from the well known fusion relations for the transfer matrices. Our method is valid for an arbitrary integrable model corresponding to the quantum group $U_q(\hat{sl}_2)$ for example for the XXZ- spin chain.