Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in framework of quantum inverse scattering method. Following algebraic Bethe ansatz diagonalise introduced using fundamental commutation relations. By acting on off-shell states and explicitly evaluating trace auxiliary space compute eigenvalues terms roots show that unwanted vanish if equations are satisfied.