  We describe the Fukaya-Seidel category of a Landau-Ginzburg model LG(2) for
the semisimple adjoint orbit of sl(2,C). We prove that this category is
equivalent to a full triangulated subcategory of the category of coherent
sheaves on the second Hirzebruch surface. We show that no projective variety
can be mirror to LG(2), and that this remains so after compactification.
