Open Access Open Access  Restricted Access Subscription Access

A note on Jacquet functors and ordinary parts

Claus Sorensen

Abstract


In this note we relate Emerton's Jacquet functor $J_P$ to his ordinary parts functor $\operatorname{Ord} _P$, by computing the χ-eigenspaces $\operatorname{Ord} ^{\chi }_P$ 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 $J_P$, with potential applications to local-global compatibility in the $p$-adic Langlands program in the ordinary case.


Full Text:

PDF

References


Breuil, C. and Herzig, F., Ordinary representations of $G(mathbb Q_p)$ 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




DOI: http://dx.doi.org/10.7146/math.scand.a-26363

Refbacks

  • There are currently no refbacks.
This website uses cookies to allow us to see how the site is used. The cookies cannot identify you or any content at your own computer.
OK


ISSN 0025-5521 (print) ISSN 1903-1807 (online)

Hosted by the Royal Danish Library