Cohomologically induced distinguished representations and cohomological test vectors
Representation Theory
2019-09-10 v3 Number Theory
Abstract
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 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.
Keywords
Cite
@article{arxiv.1111.2636,
title = {Cohomologically induced distinguished representations and cohomological test vectors},
author = {Binyong Sun},
journal= {arXiv preprint arXiv:1111.2636},
year = {2019}
}
Comments
We still do not have a proof of "Theorem 4.3" of Version 1. The following correction is made in this version: the invariant bilinear form in the proof of Lemma A.4, which is incorrectly used in the last version, is now changed to an invariant inner product