Emerton’s Jacquet Functors for Non-Borel Parabolic Subgroups
نویسندگان
چکیده
This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. 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 ofM 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 [Eme06b] by constructing eigenvarieties interpolating automorphic representations whose local components at p are not necessarily principal series. 2010 Mathematics Subject Classification: 11F75, 22E50, 11F70
منابع مشابه
A Note on Jacquet Functors and Ordinary Parts
In this note we relate Emerton’s Jacquet functor JP to his ordinary parts functor OrdP , by computing the χ-eigenspaces Ord χ P for central characters χ. This fills a small gap in the literature. One consequence is a weak adjunction property for unitary characters χ appearing in JP , with potential applications to local-global compatibility in the p-adic Langlands program in the ordinary case.
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