  For a finite-dimensional simple Lie algebra $\mathfrak{g}$, let
$U^+_q(\mathfrak{g})$ be the positive part of the quantized universal
enveloping algebra, and $A_q(\mathfrak{g})$ be the quantized algebra of
functions. We show that the transition matrix of the PBW bases of
$U^+_q(\mathfrak{g})$ coincides with the intertwiner between the irreducible
$A_q(\mathfrak{g})$-modules labeled by two different reduced expressions of the
longest element of the Weyl group of $\mathfrak{g}$. This generalizes the
earlier result by Sergeev on $A_2$ related to the tetrahedron equation and
endows a new representation theoretical interpretation with the recent solution
to the 3D reflection equation for $C_2$. Our proof is based on a realization of
$U^+_q(\mathfrak{g})$ in a quotient ring of $A_q(\mathfrak{g})$.
