  We determine the invariants, with arbitrary determinant twists, of the
parabolic subgroups of the finite general linear group GL_n(q) acting on the
tensor product of the symmetric algebra and the exterior algebra of the natural
GL_n(q)-module V. In addition, we obtain the graded multiplicity of the
Steinberg module of GL_n(q) in the tensor product of the symmetric algebra and
the exterior algebra of V, twisted by an arbitrary determinant power.
