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On Jordan-Hölder series of some locally analytic representations


Authors: Sascha Orlik and Matthias Strauch
Journal: J. Amer. Math. Soc. 28 (2015), 99-157
MSC (2010): Primary 22E50, 11S37, 22E35; Secondary 20G05, 20G25, 17B35, 17B15
DOI: https://doi.org/10.1090/S0894-0347-2014-00803-1
Published electronically: July 2, 2014
MathSciNet review: 3264764
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Abstract: Let $G$ be a split reductive $p$-adic group. This paper is about the Jordan-Hölder series of locally analytic $G$-representations which are induced from locally algebraic representations of a parabolic subgroup $P \subset G$. We construct for every representation $M$ of $\textrm {Lie}(G)$ in the BGG-category ${\mathcal O}$, which is equipped with an algebraic $P$-action, and for every smooth $P$-representation $V$, a locally analytic representation ${\mathcal F}^G_P(M,V)$ of $G$. This gives rise to a bi-functor to the category of locally analytic representations. We prove that it is exact and give a criterion for the topological irreducibility of ${\mathcal F}^G_P(M,V)$ in terms of $M$ and $V$.


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Additional Information

Sascha Orlik
Affiliation: Fachbereich C - Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
Email: orlik@math.uni-wuppertal.de

Matthias Strauch
Affiliation: Indiana University, Department of Mathematics, Rawles Hall, Bloomington, Indiana 47405
MR Author ID: 620508
Email: mstrauch@indiana.edu

Received by editor(s): February 13, 2013
Received by editor(s) in revised form: December 4, 2013, and December 17, 2013
Published electronically: July 2, 2014
Additional Notes: M. S. would like to acknowledge the support of the National Science Foundation (award numbers DMS-0902103 and DMS-1202303).
Article copyright: © Copyright 2014 American Mathematical Society