arXiv 1111.26362011-11math.RTmath.NT

Cohomologically induced distinguished representations and cohomological test vectors

Binyong Sun

备注：: 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
发表信息：: Duke Math. J. 168, no. 1 (2019), 85-126
DOI：: 10.1215/00127094-2018-0044

英文摘要：

Let $G$ be a real reductive group, and let $χ$ be a character of a reductive subgroup $H$ of $G$. We construct $χ$-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.

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