  Let $G$ be a real reductive group, and let $\chi$ be a character of a
reductive subgroup $H$ of $G$. We construct $\chi$-invariant linear functionals
on certain cohomologically induced representations of $G$, and show that these
linear functionals do not vanish on the bottom layers. Applying this
construction, we prove two archimedean non-vanishing assumptions, which are
crucial in the study of special values of L-functions via modular symbols.
