  Let $M$ be a compact K\"ahler manifold equipped with a pre-quantum line
bundle $L$. In [9], using $T$-symmetry, we constructed a polarization
$\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on
toric manifolds. In this paper, we obtain the following results for the quantum
space $\mathcal{H}_{\mathrm{mix}}$ associated to $\mathcal{P}_{\mathrm{mix}}$.
First, $\mathcal{H}_{\mathrm{mix}}$ consists of distributional sections of $L$
with supports inside $\mu^{-1}(\mathfrak{t}^{*}_{\mathbb{Z}})$. This gives
$\mathcal{H}_{\mathrm{mix}}=\bigoplus_{\lambda \in
\mathfrak{t}^{*}_{\mathbb{Z}} } \mathcal{H}_{\mathrm{mix}, \lambda}$. Second,
the above decomposition of $\mathcal{H}_{\mathrm{mix}}$ coincides with the
weight decomposition for the $T$-symmetry. Third, an isomorphism
$\mathcal{H}_{\mathrm{mix}, \lambda} \cong H^{0}( M//_{\lambda}T,
L//_{\lambda}T)$, for regular $\lambda$. Namely, geometric quantization
commutes with symplectic reduction.
