Cohomologically induced distinguished representations and a non-vanishing hypothesis for algebraicity of critical L-values

Details Cohomologically induced distinguished representations and a non-vanishing hypothesis for algebraicity of critical L-values Cohomologically induced distinguished representations and a non-vanishing hypothesis for algebraicity of critical L-values

2011-11-11

arxiv.org/abs/1111.2636v1

Mathematics

Representation Theory

Scientific paper

Let $G$ be a real reductive group with an involution $\sigma$ on it. Let $H$ be an open subgroup of $G^\sigma$ with a character $\chi$ on it. Associated to a "theta stable", "$\sigma$-split" parabolic subalgebra, and using the Zuckerman functor, we construct representations of $G$ together with $\chi$-equivariant linear functionals on them. We apply this construction to prove a non-vanishing hypothesis of H. Grobner and A. Raghuram in the study of algebraicity of critical L-values.

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