  We discuss some aspects of the composition structure of twisted Verma modules
for the Lie algebra $\mathfrak{sl}(3, \mathbb{C})$, including the explicit
structure of singular vectors for both $\mathfrak{sl}(3, \mathbb{C})$ and one
of its Lie subalgebras $\mathfrak{sl}(2, \mathbb{C})$, and also of their
generators. Our analysis is based on the use of partial Fourier tranform
applied to the realization of twisted Verma modules as $\mathrm{{D}}$-modules
on the Schubert cells in the full flag manifold for $\mathrm{SL}(3,
\mathbb{C})$.
