We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the reflection equation and by short exact sequences of intertwiners of the standard Borel subalgebras of $U_q(\widehat{ \mathfrak{ sl}_2})$. The resulting Bethe equations are the same as those arising from Sklyanin's algebraic Bethe ansatz.
Categories: math-ph math.MP math.QA math.RT
