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- W4284964922 abstract "We prove that cuspidal automorphic D-modules have non-vanishing Whittaker coefficients, generalizing known results in the geometric Langlands program from GL_n to general reductive groups. The key tool is a microlocal interpretation of Whittaker coefficients. We establish various exactness properties in the geometric Langlands context that may be of independent interest. Specifically, we show Hecke functors are t-exact on the category of tempered D-modules, strengthening a classical result of Gaitsgory (with different hypotheses) for GL_n. We also show that Whittaker coefficient functors are t-exact for sheaves with nilpotent singular support. An additional consequence of our results is that the tempered, restricted geometric Langlands conjecture must be t-exact. We apply our results to show that for suitably irreducible local systems, Whittaker-normailzed Hecke eigensheaves are perverse sheaves that are irreducible on each connected component of Bun_G." @default.
- W4284964922 created "2022-07-10" @default.
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- W4284964922 date "2022-07-06" @default.
- W4284964922 modified "2023-09-23" @default.
- W4284964922 title "Non-vanishing of geometric Whittaker coefficients for reductive groups" @default.
- W4284964922 doi "https://doi.org/10.48550/arxiv.2207.02955" @default.
- W4284964922 hasPublicationYear "2022" @default.
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