quantum symmetric pairs with different parameters. The non-super specialization the work here amounts a reformulation of the classical Kazhdan-Lusztig theory of type C/D. This paper is a sequel of [@BW13].

A naive idea to follow [@BW13] is to find the subalgebra of $\U_q(\mathfrak{sl}_k)$, whose action on the tensor product $\VV^{\otimes m}$ centralizing the action of the Hecke algebra $\mc{H}_{D_m}$ of type D on $\VV^{\otimes m}$. Such (new) subalgebra has been constructed using the geometry of isotropic partial flag varieties of type D in [@FL14]. However the subalgebra is very involved, as expected, due to the complicated structure of isotropic flag varieties of type D, which makes it not suitable for further application to the category $\mc{O}$ of Lie superalgebras.

We realize a natural and simple way to overcome the difficulty is to first consider the Hecke algebra $\mathcal{H}^{1}_{B_m}$ of type B with unequal parameters. Let $\mathcal{H}^{p}_{B_m}$ be the Iwahori-Hecke algebra of type $B_m$ with two parameters $p$ and $q$ over $\mathbb Q(q, p)$, generated by $H^p_0, H_1, H_2, \dots , H_{m-1}$, and subject to certain relations (see ). The Hecke algebra $\mathcal{H}^{1}_{B_m}$ is the specialization of $\mathcal{H}^{p}_{B_m}$ at $p=1$. We observe that $\mathcal{H}^{1}_{B_m}$ naturally contains the Hecke algebra $\mc{H}_{D_m}$ of 