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Cohomologically induced distinguished representations and cohomological test vectors

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Sun,  Binyong
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1111.2636.pdf
(Preprint), 310KB

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Sun, B. (2019). Cohomologically induced distinguished representations and cohomological test vectors. Duke Mathematical Journal, 168(1), 85-126. doi:10.1215/00127094-2018-0044.


Cite as: https://hdl.handle.net/21.11116/0000-0004-F83F-F
Abstract
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.