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.

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

>

Published
2017-10-22
How to Cite
Sorensen, C. (2017). A note on Jacquet functors and ordinary parts. MATHEMATICA SCANDINAVICA, 121(2), 311-319. https://doi.org/10.7146/math.scand.a-26363
Section
Articles