  Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and
$U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let
$\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that
the defining relations for $U_q(\mathfrak{g})$ can be slightly modified in such
a way that the resulting algebra $U_q(\mathfrak{g};\mathcal{S})$ allows a
homomorphism onto (an extension of) the algebra
$\mathrm{Pol}(\mathbb{G}_q/\mathbb{K}_{\mathcal{S},q})$ of functions on the
quantum flag manifold $\mathbb{G}_q/\mathbb{K}_{\mathcal{S},q}$ corresponding
to $\mathcal{S}$. Moreover, this homomorphism is equivariant with respect to a
natural adjoint action of $U_q(\mathfrak{g})$ on
$U_q(\mathfrak{g};\mathcal{S})$ and the standard action of $U_q(\mathfrak{g})$
on $Pol(\mathbb{G}_q/\mathbb{K}_{\mathcal{S},q})$.
