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 ##IMG## [http://ej.iop.org/images/1751-8121/53/24/245205/aab8854ieqn1.gif] {${U}_{q}\left({\hat{\mathfrak{s}\mathfrak{l}}}_{2}\right)$} . The resulting Bethe equations are the same as those arising from Sklyanin’s algebraic Bethe ansatz.

中文翻译：

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AQ-开放自旋链的算子I. Baxter的TQ关系

我们为带有对角边界条件的开放XXZ Heisenberg量子自旋链构造了一个Q算子，并给出了Baxter的TQ关系的严格推导。该理论的关键作用是由反射方程的特定无穷维解和## IMG ## [#http：//ej.iop.org/images/1751 -8121 / 53/24/245205 / aab8854ieqn1.gif] {$ {U} _ {q} \ left（{\ hat {\ mathfrak {s} \ mathfrak {l}}} _ {2} \ right）$} 。生成的Bethe方程与Sklyanin的代数Bethe ansatz产生的方程相同。