The quantum analog of a symmetric pair: a construction in type $(C_{n},A_{1}\times C_{n-1})$

Let $\mathcal {I}$ be the ideal in the enveloping algebra of $\mathfrak {sp}(n,\mathbb C)$ generated by the maximal compact subalgebra of $\mathfrak {sp}(n-1,1)$. In this paper we construct an analog of $\mathcal I$ in the quantized enveloping algebra $\mbox {$\mathfrak {U}$}$ corresponding to a type $C_{n}$ diagram at generic $q$. We find generators for $\mathcal {I}$ and explicit bases for $\mbox {$\mathfrak {U}$}/\mathcal {I}$.