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Let $\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$ and $\mathcal{O}(SO_q(2n+1))$be the quantized algebras of regular functions on the Lie groups$\mbox{Spin}(2n+1)$ and $SO(2n+1)$, respectively. In this article, we provethat the Gelfand-Kirillov dimension of a simple unitarizable$\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$-module $V_{t,w}^{\mbox{Spin}}$ isthe same as the length of the Weyl word $w$. We show that the same result holdsfor the $\mathcal{O}(SO_q(2n+1))$-module $V_{t,w}$, which is obtained from$V_{t,w}^{\mbox{Spin}}$ by restricting the algebra action to the subalgebra$\mathcal{O}(SO_q(2n+1))$ of $\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$.Moreover, we consider the quantized algebras of regular functions on certainhomogeneous spaces of $SO(2n+1)$ and $\mbox{Spin}(2n+1)$ and show that itsGelfand-Kirillov dimension is equal to the dimension of the homogeneous spaceas a real differentiable manifold.

Computation of Gelfand-Kirillov dimension for $B$-type structures