#### DOCUMENTA MATHEMATICA, Vol. 16 (2011), 1-31

Richard Hill and David Loeffler

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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