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 JP to his ordinary parts functor OrdP, by computing the χ-eigenspaces OrdχP 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 JP, with potential applications to local-global compatibility in the p-adic Langlands program in the ordinary case.
References
Breuil, C. and Herzig, F., Ordinary representations of G(mathbbQp) and fundamental algebraic representations, Duke Math. J. 164 (2015), no. 7, 1271–1352. https://doi.org/10.1215/00127094-2916104
Emerton, M., Jacquet modules of locally analytic representations of p-adic reductive groups. I. Construction and first properties, Ann. Sci. École Norm. Sup. (4) 39 (2006), no. 5, 775–839. https://doi.org/10.1016/j.ansens.2006.08.001
Emerton, M., Jacquet modules of locally analytic representations of p-adic reductive groups II. The relation to parabolic induction, J. Inst. Math. Jussieu (to appear).
Emerton, M., Ordinary parts of admissible representations of p-adic reductive groups I. Definition and first properties, Astérisque (2010), no. 331, 355–402.
Emerton, M., Ordinary parts of admissible representations of p-adic reductive groups II. Derived functors, Astérisque (2010), no. 331, 403–459.
Schneider, P. and Teitelbaum, J., Algebras of p-adic distributions and admissible representations, Invent. Math. 153 (2003), no. 1, 145–196. https://doi.org/10.1007/s00222-002-0284-1
