Geodesic
Emerton's Jacquet functors for non-Borel parabolic subgroups
Documenta mathematica, Tome 16 (2011), pp. 1-31.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper studies Emerton's Jacquet module functor for locally analytic representations of $p$-adic reductive groups, introduced in citeemerton-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 citeemerton-interpolation by constructing eigenvarieties interpolating automorphic representations whose local components at $p$ are not necessarily principal series.
Classification : 11F75, 22E50, 11F70
Keywords: eigenvarieties, $p$-adic automorphic forms, completed cohomology 
@article{DOCMA_2011__16__a33,
     author = {Hill, Richard and Loeffler, David},
     title = {Emerton's {Jacquet} functors for {non-Borel} parabolic subgroups},
     journal = {Documenta mathematica},
     pages = {1--31},
     publisher = {mathdoc},
     volume = {16},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a33/}
}
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Hill, Richard; Loeffler, David. Emerton's Jacquet functors for non-Borel parabolic subgroups. Documenta mathematica, Tome 16 (2011), pp. 1-31. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a33/