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We consider intertwining relations of the augmented $q$-Onsager algebraintroduced by Ito and Terwilliger, and obtain generic (diagonal) boundary$K$-operators in terms of the Cartan element of $U_{q}(sl_2)$. These$K$-operators solve reflection equations. Taking appropriate limits of these$K$-operators in Verma modules, we derive $K$-operators for Baxter Q-operatorsand corresponding reflection equations.

Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators