A note on Jacquet functors and ordinary parts
DOI:
https://doi.org/10.7146/math.scand.a-26363Abstract
In this note we relate Emerton's Jacquet functor $J_P$ to his ordinary parts functor $\operatorname{Ord} _P$, by computing the χ-eigenspaces $\operatorname{Ord} ^{\chi }_P$ for central characters χ. This fills a small gap in the literature. One consequence is a weak adjunction property for \textit {unitary} characters χ appearing in $J_P$, with potential applications to local-global compatibility in the $p$-adic Langlands program in the ordinary case.
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