Emerton's Jacquet Functors for Non-Borel Parabolic Subgroups

This paper studies Emerton's Jacquet module functor for locally analytic representations of $p$-adic reductive groups, introduced in \cite{emerton-jacquet}. When $P$ is a parabolic subgroup whose Levi factor $M$ is not commutative, we show that passing to an isotypical subspace for the derived subgroup of $M$ gives rise to essentially admissible locally analytic representations of the torus $Z(M)$, which have a natural interpretation in terms of rigid geometry. We use this to extend the construction in of eigenvarieties in \cite{emerton-interpolation} by constructing eigenvarieties interpolating automorphic representations whose local components at $p$ are not necessarily principal series.

2010 Mathematics Subject Classification: 11F75, 22E50, 11F70

Keywords and Phrases: Eigenvarieties, $p$-adic automorphic forms, completed cohomology

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