Let be a real reductive group, and let be a character of a reductive subgroup of . We construct -invariant linear functionals on certain cohomologically induced representations of , and we show that these linear functionals do not vanish on the bottom layers. Applying this construction, we prove two Archimedean nonvanishing hypotheses which are vital to the arithmetic study of special values of certain -functions via modular symbols.
"Cohomologically induced distinguished representations and cohomological test vectors." Duke Math. J. 168 (1) 85 - 126, 15 January 2019. https://doi.org/10.1215/00127094-2018-0044